Renekton was the first champion released since late September of 2010 that I have actually enjoyed, and I took to him nicely. While he did suck at immediate release, his buff made him viable, and now he is great fun to play. I have finished many games with scores such as 11/1/5 or 24/6/10.

Renekton's Role On The Team: He is a damage-dealer, chaser, and assassin. He is great for charging after initiation and picking off high-priority targets. Do not try to play him as a tank or support, that is not his specialty. Do not try to play him as an auto-attack character, that is not his design. While these other builds can still be viable in some circumstances (such as if you are forced to be the team's tank), they do not come anywhere close to letting Renekton reach his full potential.
(For further explanation of why Renekton should not be built as a tank or auto-attacker, see the Item section)

If you feel you might enjoy cleaving off faces as a giant crocodile, keep reading, and...

PREPARE TO UNLEASH THE WRATH OF THE CROCODILE GOD!

The runes that I have been dominating with are not exactly typical, but they've worked well for me.

Quintessences and Marks
Greater Quintessence of Desolation Greater Quintessence of Desolation x 3
Greater Mark of Desolation Greater Mark of Desolation x 9
Total: +25 Armor Penetration
Armor Penetration benefits Renekton enormously, especially early-game. Your sources of damage (aside from the damage of Dominus) are all physical, so you need that Armor Penetration to do the most damage possible.

Seals
Greater Seal of Defense Greater Seal of Defense x 9
Total: +24 Armor at Lv. 18 (~1.35 per level)
Since you are a melee character, you are more frequently hit by auto-attacks, and having extra armor can really help you absorb that damage. In addition, my build includes 1-2 items with Armor, thus makes you moderately durable without sacrificing damage. Near the end of the game, you will have over 100 Armor without buying any tank items.
(Dodge Seals are a common choice, but I would personally prefer mitigation over a small chance to dodge. Dodge works best on tanks or champions built for dodge, such as Jax and Sivir. Renekton is neither of those.)


Glyphs
Greater Glyph of Celerity x 9
Total: +8.64% cooldown reduction at Lv. 18 (~0.48 per level)
While many prefer flat cooldown reduction , I prefer scaling. Why? Because early-game, your Ionian Boots and Brutalizer will give you enough, but late game, you will struggle to hit 40%. Glyphs of Celerity push it pretty close.

Masteries
My Masteries should be easy to understand, but I will offer clarification on a few points.

Why don't I take Nimbleness or Greed? Because they aren't extremely effective on Renekton. He farms well enough to not need gold, and he isn't really a viable Dodge champion.

Why Archaic Knowledge? Because Dominus lasts 20 seconds, and for that entire duration, you deal magic damage to people around you. The spell penetration means you Dominus hits just a little bit harder, which is never a bad thing when it does 100 per second for 20 seconds.

Summoner Spells
Ghost is ridiculously useful for Renekton.
First off, the speed is great, because Renekton has no natural slowing ability and needs to catch people and stun them.
Secondly, because it allows you to ignore collision, it becomes much easier to ensure you are damaging people while Dominus is active. I have killed many people by just standing near them while my Ult is on, or by chasing them down when their health is low and my abilities are on cooldown.

Exhaust is not especially needed, I admit. If you feel to need to take something else, feel free. The main reason I take it is because the most efficient way to build my Masteries is to get Cripple.

Other viable options for Renekton's second Summoner Spell might include...

More Useful
Cleanse
Ignite
Flash

Less Useful
Heal
Teleport

Special Situation
Smite (He can jungle, but not with this build)

If you are laning with a partner, start with Boots and 3 Health Potions. Early game, speed is useful for Renekton's harassment. Since his abilities cost nothing, he just needs to stay alive, and that's what potions are for.
If for some reason you are taking a solo lane, Doran's Shield is a solid item to keep you alive. From there, just follow the normal path, picking up Ionian Boots and Brutalizer as soon as you can.

Ionian Boots of Lucidity are cheap, and a great source of cooldown reduction, which is vital early-game. The only other boots you should consider getting are Mercury's Treads, if the enemy team has a lot of CC.
The Brutalizer is your perfect early and mid-game item. It has damage, it has armor pen, and it has cooldown reduction. However, Youmuu's Ghostblade is almost a waste of money. Only upgrade to a Ghostblade if the game is dragging on and you have money to spare.
Phage provides damage, health, and your best source for a slow (aside from Red Buff). Unless you really need health and/or need a consistent slow, hold off on upgrading to a Frozen Mallet until you have finished your Bloodrazor.
Madred's Bloodrazor is a must have. Since your Ruthless Predator applies on-hit effects, you can deal ridiculous damage to anybody with a Bloodrazor in your inventory. The best way to start it is to grab a Pickaxe, but after that it doesn't matter as much.

There are honestly many ways to fill your slots. Good options include...
Black Cleaver
Last Whisper
Spirit Visage
The only items I would say you cannot do without are Ionian Boots, Brutalizer, Phage/Mallet, and Bloodrazor.

Late-game, I like to grab an item with lifesteal, usually Bloodthirster.
The downside to Bloodthirster is that you lose the stacked damage when you die, but that is why I like to get a Guardian Angel as a complementary item. It makes you much harder to kill, and more importantly, gives you insurance that you won't lose your stacks.

There are key things to remember about itemizing Renekton.
1 - He is not an auto-attacker. This means that crit and attack speed are not viable, because they do not benefit his abilities. His abilities are his source of damage, not his auto-attacks.
2 - Cooldown reduction is not that hard to max with the proper items, and greatly boosts his damage output by making his abilities recharge faster.
3 - Renekton is not a tank. If you buy defensive items, choose wisely. Don't buy more than 1 or 2, otherwise your damage will suffer immensely.

Explanation of Renekton's Design and Why These Items are Best
1 - All three of Renekton's basic abilities scale with his attack damage, and they scale dramatically. Ruthless Predator, in particular, deals 225% of his attack damage plus a flat bonus. If you are not filling most of your inventory with items that have some damage, you are wasting his damage potential.
2 - Thornmail is the classic go-to item to counter physical damage. However, it only works well if the opponent in question damages primarily through auto-attacks, since it only returns damage on normal hits. By making sure you build yourself based around damaging with abilities instead of auto-attacks, you ensure that your enemy cannot easily counter you by just buying Thornmail. This is also one of the reasons why Madred's Bloodrazor is a key item: it diversifies your damage output by making you deal magic damage and physical damage at the same time.
3 - In the same manner, by having high cooldown reduction, you increase both your capability to deal damage by means other than auto-attacks and you increase your utility. Don't forget, every single one of Renekton's abilities does more than just damage his opponent. He can heal himself, stun opponents, and chase or flee. The more cooldown reduction you have, the more often you can do these things. I have seen many people play Renekton without getting cooldown reduction, and they often fail horribly.

Cull the Meek
Early-game, this is your bread and butter. It does the best damage and heals you, and has a short cooldown. There are a few things to remember.
1 - It heals you for huge amounts when it damages Champions, but not as much against monsters or minions.
2 - You can cast it while moving and you don't stop. It is instant.
3 - You can use it to hit stealthed targets, even if you can't see them.
4 - Cull can generate a lot of fury if it hits multiple targets. Remember that.

Ruthless Predator
Mid and late-game, this is your best source of damage. Early-game you should reserve it for stunning (assuming you are confident in getting the kill) or occasionally killing minions. Here are things to keep in mind.
1 - The stun applies on your next auto-attack, rather than being a targeted ability. This means you can prepare the stun before you actually use it. This can be used to great effect in some situations, such as canceling Galio's ultimate.
2 - It applies on-hit effect. This ability is the reason I buy Madred's Bloodazor. With a Bloodrazor, you can hit someone for 8%-12% of their max health plus the ability's standard damage. This ensures you can cut down any opponent, even tanks.
It also makes Phage useful, allowing you to hold off on getting Frozen Mallet. Since it hits 2-3 times, there is greater chance to proc the item's slow.
3 - Early-game, if being pushed back, try to stun them near your tower.
4 - Can be used to build fury, but this tactic is barely used beyond early-game.

Slice and Dice
Early-game you use this mostly to harass. Later on, you use it to chase people down and kill them. It is also good for ambushing or escaping, since it can go through walls.
1 - Early game, try to use it for harassment. Slice in, use Cull and/or Ruthless Predator, then Dice out.
2 - Try to always hit something with Slice, otherwise you cannot Dice and you have to wait on the long cooldown.
3 - If you don't have something useful to use Dice on, let it wear off. This results in a shorter cooldown than if you had used Dice.
4 - Know where you can and cannot Slice/Dice through walls. I don't have a diagram, but you should be able to figure it out in-game.
5 - Using 50 Fury on Dice reduces the target's armor by a percentage. Most of the time though, its not worth wasting the fury, try to save it for Cull or Ruthless.
6 - If you are running somewhere, such as returning to a lane, use Slice to get there faster. It can't hurt.

Dominus
A very useful ultimate. Good for ganking, good in team-fights, good all around.
1 - If you are ganking, it can be viable to activate Dominus before you go in just to build up fury. But don't do it all the time.
2 - Try to not activate it until you are the sure the fight is happening. Don't activate pre-maturely or you might waste it.
3 - If you are about to be tower-dived at low health, Dominus' bonus health can save you. Stun them, heal with Cull, and use Slice/Dice to run away.
4 - 1v1, Dominus is great for turning the tide in your favor.
5 - Even if you are focusing one person, try to position yourself to damage multiple people with Dominus' continuous AOE.

EARLY GAME
Harass and farm with Cull the Meek. When using Cull, know the limits of its range, and try to hit an enemy player with it. Cull heals for much more if you hit a player.
Your standard combo is to Slice in, use Cull and/or Ruthless, and then Dice out. Since your damage is heavily limited by cooldowns, know when you can or cannot actually kill someone.

MID GAME - GANKING
Once you have Dominus and your three starter items ( , , and ), you can move out of your lane and gank people in other lanes. The basic method is as follows.
1. Sit in bush. Wait for opportunity.
2. Use Ghost and rush in, activating Dominus.
3. Use Cull the Meek to damage and build fury, preferably near minions.
4. Stun with Ruthless Predator as soon as you get 50 Fury.
5. Finish them off. If needed, use Exhaust and Slice and Dice to make sure they can't get away.

GENERAL TACTIC ADVICE
Silence is your greatest weakness. Be very cautious when fighting opponents with the ability to Silence.

It is not your job to initiate team-fights. Your job in team-fights is to hurt people with Dominus and slaughter high-priority targets such as the enemy carry or support.

Good use of Slice and Dice is key to separating good Renekton's from bad ones. You can flee, chase people down, and use it to dash through walls.

The easiest combo to quickly wipe out minions or monsters is Slice > Cull > Dice.

Cull the Meek can make it easy for Renekton to kill the dragon, compared to champions without healing abilities.

You can prepare Ruthless Predator before you actually hit someone with it. Use this knowledge wisely.
For instance, if you know Galio is going to activate Idol of Durand, prepare Ruthless before you charge in. When he taunts you, you will attack him and stun him, breaking his channel.