EDIT 5/11/11: With the 115 patch, Renekton took a big hit. Items were shifted around enough for me to re-evaluate the build. My first attempt with a redone build ended horribly, so a lot of changes are due. Bare with me while I test things out. Until then, this build is basically out of commission. If you want to read it anyway and see what helpful tips you can glean from it, please do. Comments on how it went would be great help.
I have started to work on Renekton again after a long hiatus. I'm experimenting with two options: a less tanky, more chasey DPS build focusing on AD and CDR and a tankier build depending on defense, lifesteal, and regen. The DPS build will be more practiced in the beginning. Playing a bit of Caitlyn and Pantheon gave me some ideas on physical champs I'm going to toy with. This build is still considered out of commission, but it's stepped up to work-in-progress.

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If you're read my other build (shameless plug) you know Nunu was the first champion I bought. Well, Renekton was my second champion purchase. Since his big nerf I've bought Caitlyn, Ryze, and Pantheon, but Renekton will always hold a special place in my LoLing heart. I played him when he was free for a week, and I really enjoyed the play style. He can ignore mana and AP completely for focused builds, and his abilities make farming and team fights a lot of fun.

That said, this is a bit less practiced and much more fluid than my Nunu build (shameless plug). I only bought Renekton at level 19, so this guide is a bit rougher around the edges. It will be a work in progress for a while, so please give me feedback. I don't care about votes (up or down) nearly as much as improving the build. Feedback is GREATLY appreciated.

As for the build's name, it is a reference to Fawful (http://www.mariowiki.com/Fawful). For those of you who got it, you're awesome.

Reign of Anger
Renekton's innate ability is the new Fury system. Renekon's abilities cost no mana or health. If you have more than 50 Fury points, the next ability gets a significant boost in power but drain 50 Fury. He loses Fury if he's out of combat for too long. Additionally, if Renekton's health is below 50%, he generates 50% extra Fury. His ultimate also steadily generates Fury while active.
Renekton doesn't use mana or energy. His abilities are basically free as Garen's, Katarina's, and Rumble's. It takes a little getting used to, but it's not too difficult. Being able to use abilities without fear of cost makes Renekton much more focused on cooldown reduction, which will be apparent in the items section.

Cull the Meek
Cull is a great ability. It has area damage, heals you, and builds up a TON of Fury if used in a wave of minions. With the Fury boost, it deals more damage and heals more health. Its range is a little surprising; you can be chasing someone just out of reach of your autoattacks, but Cull will still deal damage. It scales a little slowly, but the healing factor is key.
Be sure to use Cull in the middle of waves if safe, specifically between the melee minions and the magic minions, to get full effect. Don't rely on one use to heal you enough for a team fight as the health isn't that significant. A few uses will fill your HP nicely, but one hit is rarely enough.
When building offensively, Cull should function as a chasing mechanism more than healing. Use the range to your advantage and whittle away runners' health. Since its cooldown doesn't scale, put off maxing it out until midgame for team-fights when the area damage will help more. When combo-bursting, save this for after you use your Fury charge as its boost isn't as good as other abilities.
When building defensively, Cull becomes much more central to your strategy. Being a life-gain mechanism means it should be high priority for tanking. You can farm minions faster by maxing this first, and you'll rack up a bit more damage in team-fights as well.

Ruthless Predator
One of the best things about Renekton is his stunning ability. Maxed out cooldown reduction with full ranks gives you a stun every 6 seconds. In addition to the stun, you hit the enemy twice. While Furious, Renekton swings his blade three times and stuns for double the time. On top of everything else, the strikes apply on-hit effects, making it the most important ability to spam. As with any stun, strategic use is key. Stunning an opponent under a turret, when they're chasing an ally (or yourself), picking them off in team fight, etc. You should know how to use stuns.
This is your primary DPS ability. While the damage doesn't scale well at all, the cooldown reduction makes it much more effective. The stun becomes deadly when properly timed with Renekton's chasing mechanisms.
Defensively, this still is crucial to your build. It deals healthy damage and keeps the opponent around as you rack up damage (or gives you more time to run). When in team-fights, stun whoever your teammates are focusing so they can finish them off.

Slice and Dice
Another powerful thing about Renekton is his area damage dash ability. Alone, the dash only works through short walls, but if you hit an enemy through the attack (the 'Slice') you get the ability to use it again for a few seconds (the 'Dice'). With 50 Fury, Dice deals extra damage and shreds armor. An important note: Slice does not use Fury, only Dice does, allowing you to Slice in and still use a Furious ability. It has the longest cooldown of Renekton's abilities, but the scaling is only 1 second per level as of the .155 patch. Combined with Cull the Meek, Renekton is a farming machine. It also allows you to Slice into minions and Dice to the back to surprise enemy champions (and keep them there by stunning them with Ruthless Predator). As with all dash abilities, bypassing walls can be lifesaving or great ganking material.
For a DPS build, put a couple extra ranks in this after maxing your stun. You want to be able to chase as effectively as possible, and dashing a second or two earlier greatly increases your likelihood of finishing off a runner.
For a tanky build, max this last. Grab one level early on for the utility of the dash, but you shouldn't need to rely on it nearly as much.

Dominus
Renekton's ultimate is possibly the least impressive of his abilities, but it's still awesome. It grants extra health (which saves you in a lot of situations), increased attack range, and a cloud of damage per second. It lasts for 15 seconds and generates Fury passively. As with all ultimates, level it whenever possible. You'll be able to use it about once a minute when cooldown is maxed.
Dominus has the same functions for offensive or defensive builds. The most effective use of it is in a team-fight, granting extra area damage and range. Popping it while chasing can give you extra reach and a bit of area damage as well. You can use it in a pinch to heal a few hundred health, letting you escape turret fire or survive that last hit.

One thing to remember is all of Renekton's abilities build off attack damage (Dominus does have his sole AP use, but it's not worth investing anything towards). The more damage your autoattacks do, the more powerful your abilities are. You don't need mana, mana regen, AP, or magic penetration with him at all. Cooldown reduction and attack damage is all you really need to power his attacks up.

Exhaust allows you to keep an enemy champion in range for exceedingly long times by stunning with Ruthless Predator (preferably Furious for the full 1.5 second stun), using Exhaust to slow their escape during the cooldown (as well as lower their armor with the Cripple mastery), and using another RP to stun again. Definitely pick it up for an offensive build.
Fortify seems to get a bad rep. It's like everyone goes "it's a decent spell, but I'll let someone else take it." However, I'm a big believer in it (despite rarely taking it myself due to playing more offensive champs more often). The most obvious application of it is protecting your towers. Being invulnerable for a few seconds gives you a bit more time to get there and drive off the other team. The double speed firing has obvious benefits too. Something most people overlook is the 'passive' of dealing extra damage to minions, which helps you when you're building less offensive items. Taking the mastery gives your turrets splash damage, suddenly reducing the creep-buffer the other team gets by quite a bit.
Flash is great. I find Slice and Dice to be sufficient in most cases, but being able to use both Flash and Slice (and possibly Dice) you are suddenly very far from your starting point. Think of a chasing situation: you can Flash up to someone Ghosting away and stun them with Ruthless Predator, Slice through them as they run again, and Dice through again. If you have Exhaust ready still and no turret or enemy champion to stop you, you get a kill.
Flash also gives a great escape mechanism, letting you hop those walls too long for Slicing through or just getting that much farther away.

Ghost is a great for escaping on top of Slice and Dice and can lead to catching enemies unaware or saving your teammates. I used to take this over Flash all the time, but really the speed doesn't seem to help as much as hopping walls, and walking through units doesn't help when you have Slice and Dice.

Ignite is another great offensive spell, keeping opponents at low health and dealing damage over time to finish off champions with handy escapes.

Cleanse is another great spell for Renekton. Crowd control is a big problem for him. If you're not a fan of the tenacity ability, Cleanse is pretty important. Consider this instead of Fortify if you're not a fan of Quicksilver Sash.

Take Desolation for marks for armor penetration in either build. Just about every point of damage Renekton does is physical, and armor penetration is the most important thing you can get for that. Starting with 15 ArP sets up a great early game and stays useful the whole time.
Evasion seals are probably best stacked with dodge masteries for DPS builds. Triggering Nimbleness more often is very helpful in chases (and escapes). Regeneration for HP regen per level (out-performing flat HP regen by level 4) are probably worth it in tanky builds when stacked with Spirit Visage, but dodge can also be very good.
Focus glyphs for cooldown reduction is essential for Renekton. The only reason not to take this is if you rush CDR items early in your build and reaching the 40% cap early on. Magic resist or magic resist per level glyphs, but be sure to rush another CDR item or two if you take this route.
Quints should stack with your offense or defense. The best offensive quints are Desolation, bringing your starting armor pen up another 10 points. Defensively, stack them with whichever seals you took to give even more regen or dodge.

I highly recommend reading this article to see what you want in your runes pages.

DPS - 9/0/21
Let's look at all of what the Utility tree gives you:
With your glyphs and Offensive tree points, you start with about 15% CDR. You'll max out at 40% after just two items.
You get move movement speed, again letting you chase better.
You get bonus health regen, something Renekton can always use.
You get bonus buff time, experience, and gold. These aren't huge, but they definitely smooth things out.
All in all, the Utility tree covers a lot of bases for Renekton. It allows you to work in other areas much more fluidly than if you dump your points in Offense. Plus, with this set up, you free up item slots for more damage.

Tank - 9/21/0
Resistance, Hardiness, Harden Skin, Defensive Mastery, and Veteran's Scars are standard defense. Evasion and Nimbleness make team fights easier to live through. Put a point in Reinforce to make Fortify much more effective. Finish with Tenacity for a great defense boost.

Put 9 points into the Offensive tree to get crit chance and more CDR. If playing for DPS, put a point in Cripple to boost Exhaust. If playing tanky, put a point in Archmage's Savvy. Finish off with Archaic Knowledge; while Renekton doesn't deal much magic damage, one point in armor pen isn't very big while 15% magic pen does help out your ultimate.

DPS:
Doran's Shield is a strong start, giving a healthy bulk early game. Doran's Blade is a good alternative if you have a support champ in your lane. Grab Boots on your first return and finish them as Ionian Boots of Lucidity fast as possible.

After your boots are finished, grab The Brutalizer. It gives you attack damage, armor penetration, and precious cooldown reduction. With runes, masteries, Ionian Boots of Lucidity, and Brutalizer, your cooldown reduction is now maxed at 40%.

To move towards more offensive items, Trinity Force is a clear choice. If you can get Sheen all in one go, do that first. The burst damage is amazing even though the stat increases do next to nothing for Renekton. If you can't, start building up Phage as the slow, health, and damage are more important than attack speed from Zeal at first.

Next is Black Cleaver. Besides giving a bunch of AD, the AS and armor shredding are amazing for most DPS champs. Renekton takes special advantage of this by having Ruthless Predator apply on hit effects. If you don't like taking so long to make Trinity Force early game, then make this your first offensive item.

Bloodthirster is one of the best damage items in the game and gives very helpful lifesteal for survivability. With Renekton's fantastic farming capability, you should be able to keep the charges full most of the time.

Finish Youmuu's Blade if you want, but you should probably consider building your last item beforehand to save the gold.

Other items-
Phantom Dancer: Always a viable option for DPS champs. While PD doesn't give attack damage to boost his abilities, the attack speed does fuel Fury faster. The crit chance and movement speed are also amazing.
Cloak and Dagger: The new tenacity ability makes it so that you don't have to give up your Ionian Boots of Lucidity against heavy crowd control teams. C&D also gives crit chance and attack speed.
Infinity Edge: IE is a great item and can work with most DPS builds. Simply putting it in the build can work fine, increasing your AD and making you far deadlier. However, by rearranging the build a little you can easily get up to 100% crit chance with these items: 60% from 2 Phantom Dancers, 15% from Trinity Force or Youmuu's Ghostblade, and 25% from Infinity Edge. Your abilities suffer a bit overall, and if you don't take Youmuu's then you don't max your CDR. This by no means makes it bad. It's just not playing up Renekton's uniqueness or chasing power.

TANKY: (note, this has not been tested very much yet)
Starting with Doran's Shield as it allows you to rush non-armor items early on to get the most out of other areas of tankiness. Follow up with Ionian Boots of Lucidity again for CDR.
Building Philosopher's Stone early game is important to the flow of the build. The HP regen and gold keeps you going more smoothly, and later on the new Shurelya's Battlesong will give even more health and regen.
Kindlegem is tanky-Renekton's answer to The Brutalizer. There is less reason for building towards Youmuu's Ghostblade since you're not focusing on DPS. Health and CDR is just more useful for a tank, and it also builds directly into Spirit Visage for some magic resist and a big boost to your HP regen from your shield and stone (as well as your Cull the Meek).
Sunfire Aegis took a slight hit recently, but it still gives what we need for tanky options. Armor, health, and a great passive which adds up when jumping into team-fights.
Finishing up Shurelya's Battlesong is important to remember. It gives CDR and health, and the active is surprisingly helpful; use it in team-fights to chase down runners or to get your teammates to safety.
Quicksilver Sash is just like having a portable Cleanse on some nice MR. It allows you to soak up more damage from the other team's AP champs and occasionally get away from otherwise certain doom from accumulating CC.


Other items-
Thornmail: Renekton should be in the middle of team-fights rather than on the perimeter most of the time. Thornmail is a pretty cheap item, gives the best armor in the game, and has a great passive to take down DPS opponents. If you need to add some physical resistance into your game, this is a great option which can be added in at any point of your build.
Randuin's Omen: Once upon a time, each and every Renekton build had this item. You build Heart of Gold early on for armor, health, and money, you get Warden's Mail to make you harder to knock down, and you get Randuin's to become godly. Then .115 hit, and people stopped caring so much. HoG no longer grants armor, Randuin's gives less armor (though a more recent patch gave back some armor), and tanky Renekton cried a little. That said, Randuin's is still not a bad item. The ability is still there, the regen is still there, the small CDR is still there... it's just not as appealing as it was in the golden days. If you have a lot of gold coming your way, consider this over Thornmail and use the ability to make team-fights more one sided. If you're underfed and need to build cheaply, just go with Thornmail.
Force of Nature: Against heavy mage teams, FoN will let you charge right up to them. The HP regen and movement speed also improves overall tankiness regardless of team makeup. If you took Cleanse as a spell, dump Quicksilver Sash and take this instead.
Zeke's Harbinger: If laning with another physical champ, Stark's provides a great aura. Spirit Visage pumps up the regen and lifesteal you receive, and the benefits your teammates get will give you another edge in team-fights.

Please excuse the build's current state. I am not very confident in it at all after the 115 patch. If you have any recommendations, please comment below. I'd appreciate it if no one voted up or down for a while since the build is basically in renovation mode at the moment.

Renekton can be crazy fun. I have come back in a 3v3 game from losing both inhibitors (twice, each) and all turrets only to win by wiping out minions and catching the other team being greedy. The chasing ability on him can be game changing. If you plan defensively, you can play very offensively.