Ive noticed that renektons main problem is cc, but mean time u want to have as high damage as possible. Instead of getting banshees on him, i have chosen Cleanse as a summoner spell. The second Problem is his lack of speed. Yes sure, he has slice and dice, but early on it has long cd. So With ghost and the Ghorstblade, his speed is upped considerably.
I have chosen Cult of meek to skill up, because it is the skill that benefits most of skills p. Ruthless predator is stronger, but gains pretty small buffs in leveling up.
I chosen slice and dice as second because u want that speed, and armour reduction.

BUILD 1
A pure damage build.
The Brutalizer and Boots, and blue CD runes, will drop his CD pretty low around 30 % early on, and CD is a must, so obvious starter items. Then u must choose what u need most. I prefer a phage for both some damage and staying power, and the slow can negate some of the speed boost u need. But i dont get Frozen hammer yet. Now i need he need more damage, lots.
Finish ghostblade as u need the speed, and after that Black Clever synergize very well with him. A bit underdamaged item, but his fury and ruthless predator benefits from it much.
The vampiric scepter, is optional anywhere in the build. I sometimes feel that when I see the setup for opponents team, that i maybe dont need a dorans blade for some reason, and then take vampiric instead. I actually prefer it that way. After that IE, frozen hammer and Bloodthirster is obvious end game items, as this build focuses on pure damage.
I had Sword of occult in the build before, just after Brutalizer, but that should only be done if u feel it goes very well, and it seems u can end the game quickly as it can get stong very quick with renekton.

BUILD 2
I dont like Pure tank Renekton, but I got a bit more tankier build then the first one.
The trick is to try and get some damage at the same time to.
First of all, I have magic resist glyphs instead.
The beginning of the build is also similar as Build 1 the as he need CD and speed, and he
is quite strong with the early game items.
As u see here i have chosen the Veil, as this the given tanky items for renekton. MR, HP and anti cc help. After that I have chosen atmas, as i think it is a great item for renektion, and as fifth item, it synergizes well.
The last item is the big optional. Here i just put in hexdrinker as one of 3 choices what i prefer.
The 3 items I prefer here are:
Hexdrinker
Underestimated item. It gives mgic protection, and especially for renektons tanky build it is really good. Some MR and damage, and not to forget, Renektons passive has the added abilty the if he is under 50 % health, he regens 50% more fury. The hexdrinker can make him stay under 50 % some longer time.
Guardian Angel
It is the option if u feel like u need both MR and armour and dies more then is necessary in teamfights. U initate , u dies rest of the team lives.
Sunfire Cape
If u meet a more AD team, and u notice u can stay in the fray for longer times. If the team u meet is very tanky, i usually get this before atmas. This synergizes very well renekton, and those that like an Pure tankbuld often get this as one of the first items.

There are one item I have overseen and it is Randuin's Omen
It is very good on Renekton, and is probably as good as the other items,
but i just likes the other items more. Ofc, If the other team is very AD heavy, with maybe 1 or 2 ranged AD, I will usually get this, as with a sunfire u maybe cant even come close to them.

Build 3.
New build after nerf patches