Rengar is an assassin that can easily destroy team fights if he is used correctly. However, in this build we will be looking at his split pushing capabilities.
Build 1 is a squishy split pushing build with some tanky masteries for early game.
Build 2 is an all out tank build which is great for tanking towers without minions.
Build 3 is an all out aggression build with 21 points into the offence tree.

Pro
-Very strong split push with Savagery
-At max Cooldown reduction Thrill of the Hunt is on a 30 second cooldown, allowing you to get away easily
-Can assassinate squishies almost instantly
-Great Ganker
-Easy farming
Cons
-Relatively squishy compared to other Rengar builds
-Hindered by stealth detection

Flat Attack Damage reds allows you to deal more damage and push better.
Flat armor yellows gives you good defense against Physical Damage. Swap for greater seal of vitality for scaling HP if the enemy team revolves around Magic Damage.
Magic Resistance per level blues gives good resists that scale as time goes on.
2 Move speed Quints for great mobility throughout the game
Great Quintessence of Fortitude1 Flat Health Quint to improve survivability.

Build 1 and 2

9 points in the offence tree to grab the much needed Armor Penetration.
21 points in the defense tree to a lot of survivability.

Build 3

21 points in the offence tree to grab serious damage and much needed cooldown reduction.
9 points in utility to improve move speed.

- Grants the ability to leap when in stealth or bushes. Rengar builds 1 Ferocity for every ability that hits an enemy. When reaching 5 Ferocity his next ability becomes empowered.
- Next attack deals more damage and increases attack speed temporarily. Empowered does more damage and grants more attack speed.
- Deals small amount of Magic damage and gives armor and magic resist if an enemy is hit. Empowered grants 15% healing on top of the other things.
- Slows down enemy and does Physical damage. Empowered snares the enemy on top of the slow.
- Rengar goes into stealth and generates Ferocity during the time he is in stealth. Grants bonus movement speed and a massive radius in which he can see enemy champions (even those in stealth, in bushes or behind walls).

Viable Starting Items

Doran's Blade-Great cost efficiency for stats
Boots+3 Health Potion-Better roaming and an easier time dodging skill shots
Cloth Armor+5 Health Potion-Have an easier time against someone who hard counters and does Physical damage

Early Game Items

Boots-Roam around and chase down enemies
Doran's Blade-Great early game item
Wriggle's Lantern-A lot of sustain in lane and increased pushing abilities
Sheen-Take down everything faster
bonetooth necklace-Get it early to start building stacks for later

Mid Game Items

Ionian Boots of Lucidity-Increase cooldown reduction
Youmuu's Ghostblade-Should bring cooldown reduction to 40% so that Thrill of the Hunt is up at all times
Phage-Slows enemies for better chasing

Late Game Items

Trinity Force-Combines 3 items you need into one
Infinity Edge-Increase critical strike damage and attack damage
Bloodthirster-to replace Wriggle's Lantern

Maxing Savagery gives you maximum pushing capabilities and the damage needed for fights.
What you max next is up to you and who you are going against.
Maxing Battle Roar 2nd gives you a lot of armor and magic resist when you need it in team fights or duels.
Maxing Bola Strike 2nd allows you to deal more damage and chase more easily.
Level Thrill of the Hunt whenever you can (6,11,16)

The anti-champion combo is having 4-5 Ferocity and hitting the enemy champion with Savagery then taking advantage of the cooldown instant refresh (because the empowered set of skills do not share the cooldowns with the normals skills) and hitting them with a 2nd Savagery. Then following up with Battle Roar and Bola Strike

Killing towers quickly is much the same thing. Just use Savagery whenever it is up, and make sure the empowered ability used is always Savagery. Use Battle Roar and Bola Strike to hit nearby minions to increase Ferocity for an Empowered Savagery to take down tower faster.

Most Viable Summoner Spells

Great escape tool. Works well with Thrill of the Hunt
Gives you better lane presence and assassination abilities.
Can help you push even faster (seems a bit troll so I wouldn't take it)
Super Seige minions are really good at pushing and tanking towers, however Rengar's team fighting abilities are decreased.
Lets you jump into other lanes or into a team fight when you are somewhere else.
Works great with Thrill of the Hunt's move speed increase for better escapes
Improves dueling abilities and in team fights lets you completely shut down one of the enemy team's carries.

Other Summoner Spells

Could help out in lane but doesn't help much in pushing
If you are dead there is probably no good reason for you to come back to life at that instance
If you are jungling then yes
Most of your time is spent pushing
Rengar has no mana...
Doesn't give you anything you really need, you can get vision from wards or from Thrill of the Hunt

-Increase health pool by massive amount, has been calculated to be more efficient than Guardian Angel (including the revive's 750 health) when it is fully farmed.
-Better than Warmog's Armor in some cases as it drops aggression from enemies, but could also get you killed when they camp your body.
-Since Rengar already snowballs very easily you could grab it if you are confident you won't die too much.

Just auto attack! A common thing seen is sitting and the bush and using your passive to jump to minions who are low and going back into the bush to prevent from being attacked.
Use your abilities as you see fit as there is no mana to restrict you.
Savagery increases attack speed to help you farm/push faster.

As of right now Rengar is pretty much banned in most games. However the idea of split pushing is a good one and can be used to win games. Rengar in ranked is very strong, however people expect you to be roaming and killing people instead of split pushing like my guide is telling you to do.

10/12/2012-Written and Published (still playing with the idea of split push Rengar)