I've tried Renekton with many different builds and personally the one above can potentially be the most enjoyable of them all. For example: Dodge gives increased survivability (I used to play Jax so I like), triforce gives the power to chase slow and kill, some great cd reduction from the items to spam your abilities, BUT MOST IMPORTANTLY... Renekton needs attack speed to utilize his abilities. Every attack builds 5 fury so having great attack speed means you can have significantly more fury much more often. Oh and the lifesteal is very useful for staying power.

I use health quints because early game with those and a Doran's shield you can be level 1 with over 700 hp. Armor penetration to maximize the damage that reaches your enemies. Dodge seals give 6.5 dodge (with 9) so with ninja tabei your dodge is 18.5 + 2 (masteries), and obviously a little extra cd reduction helps.

Goint in to Masteries I want to remind people that this is a guide to Renekton for people who want to kill other summoners and fast, that's the mentality behind the masteries I have chosen. 9 in defense for extra 2 % dodge and nimbleness. I like the improved exhaust, crit chance stacks with trinity force, more cd reduc and AS, and also armor pen, magic pen (ult) and more dmg.

Doran's shield is good to start with as it gives more armor, regen and extra 120 hp. By the time you have to go back to base you should have enough for ninja tabei (survivability and movement speed). Whenever you don't have enough money just buy the items that are crucial (ex. you only have 400 gold when you went back so boots and health potion). Brutalizer gives good starting dmg and cd reduction. A zeal right after this increases MS to 420 as well as good starting AS and some crit chance. By now you should have built the emblem of valour so you can jungle when neccesary and give hp regen aura to teamates. Next I like to finish youmuu's for the nice speed boost (active), more AS and crit chance. When you have finished Tri Force, you can now kill almost anyone who isn't a disabler like sion, ryze or veigar. Also remember that the sheen component of tri force can be used to do disgusting ammounts of damage with ruthless predator ( sometimes upwards of 600 or 700 dmg when empwered with 50 fury). Sell dorans shield now as you need more item slots. Stinger gives more AS and cd reduction and if you have enough money you can eventually upgrade to Nashor's Tooth. Stark's fervor turns you into a beast, the lifesteal can heal quickly and is a significant bonus in teamfights. The last item to get depends on what type of game you're in, if the enemy team has lot's of melee champs then definitely get sunfire cape so that it is actually useful. Whereas in other situations useful items would be Randuins Omen, Banshee's veil and Aegis of Legion.

I'm not going to explain why I use exhaust and or ignite. This guide is to kill other champions while playing Renekton and with slice n dice he has a free flash. Also the items that I build him with give significant MS so ghost is overkill.

I don't recommend this guide for ranked play, although some might argue differently, I belive more tanky items are more crucial to success in ranked play.

PROS TO USING THIS GUIDE
Fast MS
Fast AS
Good survivablility ex. Ninja Tabei and lifesteal
Good chasing slow and killing power
Stun
AoE abilites to dmg groups
AoE ult damages everyone you touch

CONS
not very tanky
weak against disables
doesn't work if focused
needs gold to succeed
VERY WEAK AGAINST RANGED OPPENENTS WHEN LANING ALONE
it is safe to have a ranged teamate lane with you
unless you are aginst two melee laners.

Renekton is a unique melee champion as he uses fury and most likely that is why you want to play him because his fury is "cool". But his mechanic requires discretion in order to be successful. Stay back unless an obvious opportunity presents itself and you are SURE its worth it. Make sure to dole out justice to overextending enemies and know when to run from trouble regardless of what teamates tell you. Teamates will always ask,"Why did you run?" Just ignore them, because in the end the only person who can preserve yourself is you. By all means listen to your teamates, glance at the minimap every 2-5 seconds and be careful.
Also have fun.