Before you judge my builds, just look at what they are trying to do...

I think that Riven does way too much damage to be a bruiser or a tank. Even though that is effective, it's really hard to truly carry a game if you aren't shredding tanks. To truly carry a game you must instill the fear of your wind slash into their memories.

If you've ever played an assassin, then you know that you aren't supposed to initiate a fight unless you are sure that you can get in, get a kill or two, and then get out. Riven does this pretty well due to her high amounts of mobility and CC. Unlike other assassins, she has 2 sources of incredibly potent and multi-purposeful CC coming from her 3rd Q and her W; and they scale like crazy.

In other words, if you mess up, you a pretty much dead. These builds are literally taking the high-risk/high-reward play style and assessing it the ultimate test.

-Pros-
Leblanc-Level-One-Shotting Potential
High Mobility
Lots Of Room For Outplay
Very High Amounts of Damage (You can solo Baron Nashor)

-Cons-
Mistakes Are Very Unforgiving
Very Hard To Play
Extremely Vulnerable To Bruisers and Hard CC

Runes

For Top lane, Riven needs to grab as much defense as she can get because that's where bruisers live. And bruisers are the natural enemy of Assassins. Play things out correctly, and you should win lane without a hitch.

-Top-
9 Marks of AD
9 Seals of Armor
3 Glyphs of MR and 6 Glyphs of CDR
and 3 Quints of AD


-Mid-
9 Marks of AD
5 Seals of Armor and 4 Seals of CDR
5 Glyphs of MR and 4 Glyphs of CDR
and 3 Quints of AD
CDR is amazing--since you are going mid, you can get away with being a little glassier than usual. More CDR allows for you to get more damage which would otherwise be wasted on getting more CDR.

-Jungle-
9 Marks of AD
9 Seals of Armor
6 Glyphs of CDR and 3 Glyphs of MR
and 3 Quints of AD
You need armor in order to jungle effectively due to the fact that Riven's early clears are quite slow. The extra CDR you have from Runes and Masteries makes clears a bit easier to get through.

Masteries

Everything here is pretty standard, except for the masteries that are being used for Mid.
For mid, instead of using the conventional 21 9 0 page, I decided to explore the benefits of the utility branch a bit and going 21 0 9. I put the usual 21 points in on the offensive branch. I filled in the Fleet of Foot, Scout, Summoner's Insight, Alchemist, and put one point into Vampirism. Fleet of foot makes you 1.5% faster; Scout increases the cast range of trinkets by 15%; Summoner's Insight reduces the cooldown of summoner spells by a whopping 10%; Vampirism gives you 1% spell vamp and lifesteal. Vampirism spell vamps when you hit things with your Q, W and wind slash abilities.

-Top-
For Top lane, you almost always want to max your E first because everything up there does so much damage. When E is leveled 5 time, it has a base cooldown of 6 seconds which is much less with all of the CDR from the runes and materies. That's basically a dash every other second with a pretty beefy shield equal to 210 + 100% of your AD. That shield, later on in the game, will block crazy amounts of damage as it will be blocking up to almost 700 damage (this isn't even including the shield that you may get from BT).
Although W does some pretty amazing damage, and it would seem like a good idea to max second, you could never be more wrong. Since E and W scale 100% with AD, you almost don't even need to skill them for them to be extremely effective. E is a different case simply because the shorter CD is useful. W scales the same way and also has around the same CD as E does at max rank, but it pretty much cuts Riven's DPS in half. Think about it--her Q can be activated 3 times, scales differently per rank, and allows for her passive to activate more than once in short succession. It doesn't offer any shorter cooldowns when skilled at all.
Every 3 levels, Riven's passive becomes more powerful; at level 3, her passive scaling increases from having a bonus 20% AD to 25% bonus AD when it procs. Her Q ability at max rank does 90 + 60% of her AD in an AOEand resets her AA timer after every times that it's activated. So you can dish out some pretty good damage with just those two abilites alone. Her W can't provide that kind of DPS, making it the thing that you would max last.

Despite maxing E being smart, maxing Q is stronger. Once you get Q to at least level 3 and you have Brutalizer, you can all-in the enemy top laner. Brutalizer gives Riven her first powerspike, and putting levels into Q makes her just that much stronger.

-Mid-
For Mid, maxing Q and E first will be the most advantageous since it will scale your Q and make your level 6 all-in very potent and your E for the cooldown. You need the cooldown for your E to be low since enemy mid laners will constantly be trying to poke you down. They can't really do that in the early game so maxing Q is really the smarting thing to do since you DPS increases greatly with this decision.

-Jungle-
For Jungle you want to skill your abilities the same way that you would if you were going mid but for completely different reasons. I would say that you should max Q first and E second, but the fact that you are getting the devourer enchantment, maxing Q and then W allows for faster clears. You shouldn't have an issue with clears once you get the devouerer enchantment because of the attack speed that it gives you. Attack speed on Riven = faster combos.

You should probably start Krugs with Riven, smiting the large one immediately for the buff so that it will be up sooner. When you are doing Red buff you want to AA=>W immediately=>AA=>Q=>AA=>Q=>Q=>AA=>AA and continue this combo. Smite it if it's up in time because some of your health will be refunded. Proceed to clear Wraiths, then Blue, then Gromp, then Wolves, then back to Krugs to repeat this rotation. Do this until you have enough for devourer.
Since Riven starts out with a generally quite high damage kit, it's easy for her to stop jungle invades. Even against Shyvana, which is a Champion that Riven has lots of trouble dealing with later on in the game. She also deals with Lee Sin invades quite well because of the amount of DPS and CC that she is able to put out from just being level 2.
Once you get some items, you can farm insanely fast in the jungle. If someone on your team is already split pushing, if nothing is really going on, and if you haven't finished your build yet, you can literally just hop all across the map taking every camp. If done correctly, you should be able to clear the entire jungle (both sides). It's a cycle;
For this example I'm going to say that I started Blue side Krugs:
The cycle is B.Krugs=>B.Red buff=>B.Wraiths=>B.Wolves=>B.Blue buff=>B.Gromp=>P.Krugs=>P.Red buff=>P.Wraiths=>P.Wolves=>P.Blue buff=>P.Gromp...By the time you finish the purple-side's Gromp, your Krugs should just be spawning in. These kinds of camp clears are literally only possible once you have sated, Hydra, and IE. You can't do this with just BT because it doesn't provide you with any crit.

-Top-
For Starting items, it would really just depend on the situation you are in. If you are going for the farming route, Doran's Blade is the way to go as it is the safest item to get; it gives you HP, AD, and lifesteal. Longsword start is the very aggressive start that you get when you are planning to go for a level 2 or 3 all in. The extra pots allow you to play more aggressively, but at the same time don't forget that you have no HP items. Doran's Shield is the start you want if you are going against someone that does lots of damage in the early game. A Lee Sin or Garen would be good examples of when a Doran's shield would probably be the safe buy.
The itemization for this assassin in the top lane is quite a bit different from anything I've usually done with this champion, and it's all centered around the item Trinity Force. For some reason people don't build Trinity Force on Riven. It's too strong of an item to not purchase, in my opinion, because of all of the stats that it gives you. Tri-force gives Riven literally anything that she could ever want: It gives her AD, Attack speed, Critical Strike Chance, Movement speed, Health, a Sheen proc, and a Phage proc. She doesn't need the AP or mana, but that doesn't make this item a useless one. The Sheen proc in particular has caught my eye; After using an ability, your next AA will do bonus damage equal to 200% of your AD. Since most of Riven's combo relies on her ability to AA after using an ability in order to fully utilize her passive. The sheen proc from Tri-Force gives Riven's passive a steroid. Trinity force not only gives her a sheen proc, but a phage proc which is one of the things that The Black Cleaver does. Cleaver does shred armor, but with Ghostblade and Last Whisperer, armor shredding shouldn't even be an issue. Cleaver does give more CDR, but with the runes, masteries, Ghostblade, and Ionian boots of Lucidity, your CDR will be close to maxed out alredy.. If you aren't convinced yet, then just go try this build out exactly how it's lain out and tell me how it works out for you; I promise that the damage will, in fact, be real.

Cleaver can be useful though because of the stats that it gives you; if you want/need to be a bit tanker while also still doing subsequent damage, Cleaver is the right choice for you. If your team already has enough tanks, then getting a Tri-Force instead of the latter may prove to be quite strong while also providing some of the stats.

-Mid-
Since you won't be maxing E and are quite vulnerable to early-level poke in the mid lane, getting Bloodthirster as a first big item is very effective because of the large amount of lifesteal that it gives you and the overheal that you get as a shield. The amount of AD you get from Bloodthirster is higher than Hydra as well and even though you don't have the cleave and tiamat active, you won't need it until later. When you are going mid, you are going to want to play as aggressively as possible, and Bloodthirster allows you to do that.

Grabbing Ghostblade and Last Whisperer is very strong--Armor penetration is very strong--everything you do will hurt a bit more than it would if you decide to get Hydra instead of Armor Pen. These items are also more efficient than getting more damage because not only do they cost less gold to get since both of these items will cost about as much as a Hydra, the damage you do is also more efficient. Once a target has over about 50 Armor, Last Whisperer will do more damage than an IE or a Hydra; due to armor scaling per level, all of your enemies will have at least 50 Armor--even the squishies.

You need to get Hydra eventually since it's an invaluable item for Riven to get, and getting it as a fourth item is perfect. Stacking AD after you've gotten Armor Penetration is more effective than the latter, and Hydra is the item you get next. You do more damage--technically--with IE, but the cleave passive and Tiamat active will give you lots of AOE and make your ability to team-fight very strong. IE is the item you want to get last and it will make you power as a carry spike out of control due to the Critical Strike Chance and Damage buffs that you get. You will easily be hitting 1.2k+ Critical Strikes at this point, and your ultimate will do around 800 damage to targets that are at about 50% health.

-Jungle-
Building a devouerer on Riven is strong, but only if you go full crit. You don't need BT because the damage you will do is quite insane. Grab Hydra, Ghostblade, Infinity Edge, and Last Whisperer in that order--LW as a final item because the crits you can do with IE are more potent than Armor Pen. You won't need lots of CDR because when you stack Riven's passive and hit a target twice, they will be missing large portion, or all, of their HP.

Rushing Hydra is advantageous because it speeds up your ability to clear jungle camps as well as increasing the damage you do in an AOE by a great deal. Once you stack Riven's passive and then proc it with the Sated passive, you will have effectively hit 3 times, and everything around you will take this damage.

Never initiate the fights. You can't do it--not like this. The only time when it would be smart to be the first to jump in is when you are so fed that they can't do anything about it to the point where there is no outplay for the amount of DPS you have. You are simply just too vulnerable as an assassin to initiate, so what you need to do is have the supports/tanks go in first. After they initiate the fight, you want to send the tank/bruiser in. Tanks and bruisers will usually be the Top or Junglers. Once they go in, you just wait to see what cooldowns are blown on the enemy team--who blew their ultimates/summoners/long CD defensive items' cooldowns?
The point of this is to be observant of who has what available. You don't want to go in prematurely and get CC'd only to be shut down immediately. Assassins wait--you want to make sure that they can't retaliate. The amount of cooldowns that the enemy team used will definitely determine whether or not you make something happen in that fight.
You don't need peel in team fights--you are the peel. If they start trying to focus your ADC, that's your ticket; in that moment, go in and CC the whole team for your team to follow up. Make sure that they are prepared because if you chain CC sloppily, you will probably die on the spot.

If you are going to play assassin Riven, it's probably a good idea to let your team know so that they will know what to pick and how to play around you. If you have 4th or 5th pick, are forced to go jungle, have an assassin Mid, a bruiser Top, and Mage support, it's probably not a great idea to pick assassin Riven. I have concocted a ratio in which you will determine whether or not to go with this champion and build:

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The team comp of Team OP is perfect for a Top assassin Riven because there is a nice balance of damage, tank, AD, and AP while also having a great team fight in response to the Other Team. Their tanks are quite a bit tanker than ours but with a strong enough engage, none of that matters. Leona can just ult them and go (or the reverse), while Rek'Sai follows up with the knock up. While they are knocked up, Viktor would put down his W and you would follow up with all you have. Since you have a Sivir on your team your engage is just that much stronger.

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This team comp is perfect for the assassin Mid Riven. Alistar can flash-Pulverize into a Jarvan Cataclysm. You are going to want to jump into the fray almost as soon as Jarvan does because you don't want any room for retaliation. At all costs, you want to stop Azir from using his ultimate--with your damage killing him should be cake. While you deal with Azir, Tristana and Maokai can jump on Lucian. The fight would be won at that point because they simply won't have the damage to do anything back. The comp is good even though it's full AD because your team fight is just so incredibly strong. The carries won't stack armor so killing them should be easy. They have a stronger team fight overall, but your team has the stronger engage--it's strong enough decide fights before they have a say.

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This team comp is something I like to call Triple-Threat-Wind-Combo which, as you can see, contains 4 champions with knock-up abilities: Riven's 3rd Q, Kalista's Ultimate, Maplhite's Ultimate, and Yasuo's 3rd Q. This comp revolves around the full AD assassin rivals joining forces for some insane damage. The other team has an overall better team fight as their damage is more spread out, but Team OP's engage is just so insanely strong that they can get away with running a triple-threat comp like this. Apart, they are weaker than the Other Team, together they are unstoppable.

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In each of these team comps, assassin Riven wasn't just some random pick that someone made because it worked last game or they saw someone do it and wanted to try it out themselves. She fits into the comp like a missing link, or the final piece of a puzzle. She's one of the main sources of damage as well as a crucial part of their team fight.

I've found that Riven is one of the hardest champions to farm with in the Mid lane because of her lack of range. In the early levels, any ranged champion can just auto attack you if they can't hit you with any abilities and it can sometimes be quite invigorating to attempt a return trade since they can just walk away. Riven is a farming Mid laner that is like a Zed; you want to get your level 6 as soon as possible with out having to leave lane at all. You can go for an early all-in, but that's only if you think you can kill them.

CS is very important because CS = Items, and items help you scale. If you die or get poked out of lane, then you cant CS and you won't have enough for any items. In this case, you just need to have patience and if they auto attack you, get out of their range. You can't really stand in the minion wave because they will be trying to clear it with abilities--that's what you want. If they push your lane, you can freeze it and deny them poke and farm more safely.

Try to avoid any hard CC abilities without using any abilities especially shield since you need it to negate the damage of any abilities that you can't avoid very easily. An example of when to shield an ability would be something like an Annie stun or a Brand ignite since you can't avoid it's damage by just stepping out of the way. When your shield is on CD, sit back a bit until it's about to come up again because that time would be when you lose a trade since you can't negate any damage.

When going for an all-in or a trade, walk up to your enemy until you are in range to E-Q because if you use your abilities to gap close, you won't have any follow-up damage besides some really slow auto attacks. Use your Q sparingly because it's your main source of damage--once you've used it, you can't do much and are really forced to back off.

Once you get your ultimate, you can instantly go for an all-in and will almost always win it. You might not win the all-in if you let the enemy Mid laner back and they are able to grab a piece of their first item. If they back, you need to as well or else you won't be a threat to them since they will just be able to burst you down much more quickly.

Grabbing Brutalizer and Ionian Boots of Lucidity early give you lots of CDR that pretty much makes it so that your E is off cooldown every other second. It's off cooldown often enough for you to use it to stack your passive.

By the time you get Tiamat, you will be able to destroy any squishy target. Once you get Hydra, this destruction turns into deletion as you will be one-shotting squishies. The damage scaling on Riven, with so little, is quite ridiculous. So the early game is really the only thing you need to watch out for because if you don't survive it, you will be out of the game for a long time or may be the reason that it ends prematurely.