I decided to bring to Mobafire a new way of playing the late game op carry Vayne. My guide is different from all the other Vaynes so read the guide where I explain the changes I make to the classic Vayne before downvoting like a troll.
I've played her since I was about lvl 5 or 6 and she was my first champion. I've always played her this way and always have managed to outdps other carries and make whole teams fear me (once won a game where 2 of my teamates left and only me, an Ashe, and a Veigar were left and I could solo 3 of them at once thanks to this sick damage). This build is low on defense but the loss is worth it considering the high amount of damage you will be obtaining.
I'm still working on design details and reconsidering my runes (I explain why in the rune section) but the build won't be changing that much anyway.
I don't play ranked and this is not meant to be used in ranked games. People keep telling me I will get raped at ranked games if I build this way but I don't think so as long as you get good players in your team. I've played ranked already with Vayne following this build and I've owned my lane every game. I just lose all the games I play because I'm stuck at elo hell where I keep getting teamed up with trolls or noobs. I'll let you know if it's a good build for ranked once I get out of elo hell.
This is my first guide by the way and will always be adding and improving stuff till I learn to make epic guides.
English is my second language so I might get mistakes from time to time. Let me know at the comment section.
Hope you enjoy my guide :D

"This dude is a noob. No armor and no magic resist runes?"
Vayne is a massive damage champion. Why not make it higher? You should always have a tank to get the damage you're supposed to take and since your Final Hour grants you temporal stealth when using Tumble they won't be landing all their attacks on you.
So Vayne must focus on increasing her damage and killing faster so her tank doesn't need to worry about dieing.
I got this idea from a guide here in mobafire. I've been looking for it to thank the one who made the guide but I can't find it now.

Explained one by one.

Greater Mark of Armor PenetrationGreater Mark of Armor Penetration: For tanks. More armor pen makes their armor build useless if combined with Last Whisper or Black Cleaver.
Greater Seal of Attack Damage: Just more damage. No need to explain.
Greater Glyph of Attack Speed: More attack speed = faster Silver Bolts and faster kills.
Greater Quintessence of Attack Damage: Same as Greater Seal of Attack Damage.
Greater Mark of Attack Damage: Just more damage.
Greater Seal of Attack Speed: Might compensate for the lost armor pen if you get attack damage marks since more speed means more Silver Bolts and more true damage to tanks.

Some runes are missing on the list (or at least Greater Seal of Attack Damage is) so I'll set a different rune meanwhile.

Playing everyone else's runes

The runes I placed on my build are excellent for Vayne because of the massive damage but I've noticed they're not that great for other AD champions so maybe I will change my runes to the ones every Vayne player uses but not because they're better for Vayne (because I still think the others are better) but because of the other AD champs I got since I mainly play AD carry and AD tank. Might not even change it ever, still doing great with my rune set :D

Items all Vayne must buy (Core items)

Berserker's Greaves: Obviously.

The Bloodthirster: Lifesteal helps survive and also let's you heal killing dudes in the jungle if you don't have money to buy new items yet. The attack damage a bloodthirster will give you will make enemies fear you.

Phantom Dancer: More Attack Speed helps you land your third hit and do Silver Bolts faster so people will fear you.

Infinity Edge: Maybe not so necessary as the previous but it still gives you a massive boost to your damage.

The Black Cleaver: Now this item is not a situational. With it's new stats it sure beats Last Whisper since it gives you more armor pen and more attack damage (which are all stats on Last Whisper) plus some health and cooldown reduction.

Situational Items

Frozen Mallet: Frozen Mallet gives you damage but I don't like it because of the damage but for the health. It also gives you 700 health and slows enemies down (that plus your Night Hunter will help you hunt them down pretty fast). The 700 health is useful because of her being easy to kill, making her last a bit longer but still getting some more damage. Now not that great with the upgrade made to Black Cleaver and the new item Blade of the Ruined King. If you get them both maybe Frozen Mallet won't be needed that much for resistance.

Guardian Angel: This is pretty much a who-fed-Kat (or any other champ) item because reviving after getting killed by a fed champ might be an advantage to kill him when reborn. It will make you survive teamfights where you get focused and die fast, they will move on to attack the others and then you will come back and kill them all. Also, when you get ganked pushing a lane by yourself (a thing you should not do but all Vayne's still do it from time to time lol) you might still get a chance to get out of there. Also, some armor and magic resist are always helpful.

Wit's End: Just for annoying Teemos placing his Noxious Trap all around the map. It's a good choice because, like Frozen Mallet still boosts your damage giving you a bit more Attack Speed.

Blade of the Ruined King: This new item helps a lot, not just because of the lifesteal but because of both of it's unique effects. They both heal you and deal a lot of damage. This means it might keep you alive quite a while (maybe make you immortal) on 1v1 fights and maybe even while fighting 2 people. Recently it got buffed a lot more and it now helps do a lot more damage. It could be replace Phantom Dancer as long as you get Infinity Edge to have crit chance or you can just add it but still buying the core items.

Mercurial Scimitar: Nice to clear all CC's, Ignite, Deadly Venom, etc. you have and will also give you some magic resist and damage. This item is specially good when you're going against a Teemo because of the mushroom spam.

Trinity Force: This item is also very nice to do more damage thanks to Sheen's passive and it's attack damage. It also gives you a nice amount of survivability with some health and it gives you some mana in case you get mana hunger in late game (though you shouldn't) I don't recommend it because it has stats Vayne doesn't need and I consider it too expensive to place it as a core item; this build is already too expensive. Some Vayne players might consider it good for playing style so I don't completely ditch it.

Runaan's Hurricane: Massive attack speed (70%) and a lot of aoe damage. Haven't bought the item yet but I guess item is great for Vayne mainly because of the aoe making farming easier. This item won't stack Silver Bolts, but still do massive aoe damage, good for teamfights and farming. Once made a quadra focusing the tank because the lose arrows/bolts were going for the ADC's. After taking tank and the other ADC down I just chased the lose Soraka down and got the quadra. A friend had started the fight (1v4) and died before I got there so maybe the ADC's were missing about 1/4 of their HP but then I jumped in 1v4 and took them out.
The optional 2x Doran's Blade: Well they're great since they give you more damage and "lifesteal" (5 hp per hit now and not lifesteal) to intimidate more and resist more in your lane but you will have to sell them later and that might make you lose some money. This build is already too expensive to go using money on items you will be selling back later. It's not a bad choice since they can help you get fed faster so it might be used by some people as an inversion by doing more damage and get more money.

I feel I'm missing some items. I'll add them whenever I remember.

Spells I would use.

Flash is always needed to get out of a fight and save yourself or to catch down an enemy that's too far away.

Ignite is nice to kill an running enemy without the need to chase him down or to reduce his Heal and kill him (if luckily used before the heal).

Heal because Vayne is squishy and might get killed easily and a nice heal might save your a**.

Other good spells.

Exhaust will be mostly used to run away or catch up and kill but I don't recommend this one. Besides, getting Frozen Mallet will help you catch up quickly with an enemy or slow them down to run away using Condemn which should also slow them.

Ghost has pretty much the same uses as Exhaust so I would not recommend it either.

Cleanse might be good to escape from a fight or saving your butt like Heal but you're always supposed to have a tank nearby so I wouldn't get it either. Tumble and Flash can help a lot to get away after stuns like Sion's or aoe slows like Miss Fortune's or Gangplank's. I don't prioritize it too much because at teamfights they will CC the tank first (if they are silly enough) since he's supposed to start the fight and they will spam all their skills on him. If you're playing ranked or draft pick and you see you will be going against a Taric or another heavy CC enemy then get the Cleanse but other than that I think it's not necessary. Already explained at comments that you're not supposed to initiate teamfights and that means the enemy will waste most of their CC on the rest of the team before you actually join in.

Barrier is good when laning vs champions like Nidalee that have skillshots you can see coming towards you so you can activate the shield to avoid a lot of damage. I personally never use it because I don't have the reflexes needed to use this spell correctly. I can only react in time to dodge with Tumble... If I have to focus on using Barrier in time to protect myself I will get all messed up.

Don't get the other spells ever.

Skill priority

Final Hour > Tumble > Silver Bolts > Condemn

Priority explained

Why Tumble over Silver Bolts?

Tumble is a better skill to start the game. In early game you mostly get close, hit enemy once or twice and back away to avoid the both of them charge at you; so Vayne could do the Basic Attack, Tumble, Basic Attack combo (since Tumble resets Basic Attack making you hit twice in no time) in a short while or just use Tumble to poke for a while until you can get a safe kill. Also it's good to avoid skillshots that might hurt you a lot (like Nidalee's spear). Higher rank in Tumble lowers cooldown so it helps a lot more to kill faster than Silver Bolts.
Silver Bolts, on the other hand, needs 3 hits to be useful and that is dangerous because the time it takes you to land 3 hits to do some significant damage to them might be enough for them to charge at you and get a kill. Number 1 Vayne guide in Mobafire understands me in skill priority. By the way, I've taken almost half the HP of a enemy champion using just Tumble. Last time I remember doing that the enemy was a Fiora. Maybe she had a bad build but still... Almost half health in one hit thanks to Tumble? All ADC should fear Vayne with this build since they usually don't build a lot of armor.

I leave Condemn for last since we are only interested in the pushback and the stun, which will not improve with any rank.

Don't follow each of the builds I got exactly. Instead, mix them up using the runes from build 3 and the masteries from build 1, for example. Be creative and make your own build mixing the different builds I got around.

I explained this all around the guide but people still complain saying it's stupid. I'm going to explain them all again here in one single subsection so you can read them all at once.
Well I made my build mixing up all top 10 guides in Mobafire where I took some differences I considered better for Vayne
I never prioritize defense since you're supposed to have a support to take all the dmg for you or heal you after taking some heavy blows. In teamfights they will focus you (also at laning but not so intense since it's just 2 people) but it'll be hard since you will be dissapearing all the time having your Final Hour up and spamming Tumble like all Vayne should do (and you can't say I'm wrong about spamming it). Also, having your ult up you will kill them all in no time since I prioritize damage more than any other Vayne.
I can easily outdps any other ADC I play against unless he gets more fed than me or I don't get fed at all. Maybe you might die more with this build (though is no big deal actually) but you will kill a lot faster and do more damage to help your team making those deaths worth it (unless you get surprised by 3 enemies and can't manage to do a thing ofc).
About the runes: No defense runes because, as I explained before, I prioritize damage to destroy them quickly. I might change the runes a bit placing attack dmg at marks and attack speed at seals (or leave them as attack damage) or something but they will always be physical dmg runes.
The only 1 point on armor issue is already explained at the masteries section and it's quite long so I don't feel like explaining again in here.
I'm not saying the other build is bad, I just say I consider my build might be more effective but I can't say it's a bad choice to go the other build.

AP Vayne? WTF?!
A friend of mine talked to me about that Spellsword mastery and told me: "What if you play Vayne full AP, using AP masteries and runes? That Spellsword thing might make it worth it."

I don't dare try it out but whoever feels like doing it go ahead and tell me how it goes. I didn't dedicate much time to the runes, masteries, and items because I don't play AP and I don't know how it would be best if this build could actually work.

Happy trolling.

Season 3 actually brings no changes to Vayne, or at least I wouldn't change her build. Black Cleaver gives you less health now but it gives you a total of 1% more armor pen so I guess is no big deal. Another change that might affect is that Bloodthirster in now 200 gold more expensive... But that won't make us ADC's stop buying it obviously :D
I haven't actually tried Season 3 yet but that's what I expect will happen with my build.

Too lazy to do some coding at all in this chapter. Only did some links to the items and champion name.

As of patch 3.03 I'll start adding the changes that patches make on Vayne and if the patch will change her build or gameplay. Every patch's icon will be the newest champion even if it was released a few patches before.

Patch 3.03:
Vayne just gets "improved" (made it a bit easier for us). Now her Tumble uses up less mana and that helps the mana issues she had early game. Also, now she has more mana per level which also helps with these issues. Haven't tried the new Blade of the Ruined King but I'll let you know as soon as I try it but I don't think (just by checking the stats) the changes on the blade are worth changing the build. You already have enough attack speed and massive damage. Also made some changes to the guide I had forgotten to change before.
Patch 3.04:
No direct effects on Vayne at all this patch but Blade of the Ruined King does get changed. Some of its stats are lowered and price is higher but this doesn't make the item a lame item now. Still a good one you can replace with Phanton Dancer or Ruunan's Hurricane.
Patch 3.5:
No effects at all. All ADC items remain the same and Vayne remains the same aswell. Didn't update earlier patches because it was the same addition. Other bottom lane champions have had some changes but it doesn't really affect her that much.

Just want to thank all the Vayne guides that are already around in Mobafire. I took a bit from all of them and made my own way of playing Vayne and now I'd like to share it.
Too bad I didn't found the one that made me decide to go differently on runes because all the guides say Vayne must get armor and magic resist (actually everyone gets those runes for all ADC's) but he/she and I didn't agree lol.
Also thanks to Die Fellnase who recommended me to try Runaan's Hurricane and consider it a must for Vayne. I totally agree with him on it.