Hello, I am Bennygump and I will be taking you through how I build Rengar and why.

On every wall of his den, the trophy hunter Rengar mounts the heads, horns, claws, and fangs of the most lethal creatures in Valoran. Though his collection is extensive, he remains unsatisfied, tirelessly seeking greater game. He takes time with every kill, studying his prey, learning, and preparing himself for the next encounter with the one monster he never managed to defeat.

Rengar never knew his real parents, but was raised by a human who was revered as a legendary hunter. He was an ideal pupil, intently absorbing the lessons of his father, and improving them with his uncanny feral instincts. Before his mane had fully grown, Rengar set off on his own and claimed a wide territory for himself. Along its perimeter, he mounted the skulls of his slain prey - a warning to would-be aggressors. He thought undisputed reign of a region would fulfill him, but instead, he grew restless. No beasts in his domain proved challenging prey, and without formidable adversaries to push his limits, Rengar's spirit waned. He feared that no worthwhile game remained, that he would never again feel the thrill of the hunt. Just when things seemed their bleakest, he encountered the monster. It was a disturbing, alien thing, distinctly out of place in his world. It bore huge scything claws and devoured any animal that strayed across its path. Overzealous at the prospect of a challenge, Rengar ambushed the monster in haste. It far outclassed anything he'd hunted before. Their fight was savage, and each suffered crippling wounds. Rengar lost an eye, but the most grievous blow was to his pride. He had never before failed to make the kill. Worse yet, the severity of his injuries forced him to retreat. Over the following days, he hovered on the threshold between life and death. He was wracked with pain, but beneath it, he felt a glimmer of joy. The hunt was on. If such powerful beings existed in the world, he would find them, and stack their heads high. The monster, however, was a kill he wanted to savor. On his den's largest wall, he reserves a space for the beast's head, a trophy he swears will one day be the centerpiece of his collection.

"Prey on the weak and you will survive, prey on the strong and you will live."
-Rengar

PROS

Can slow and root when enemies are running.
If low on health can use your roar and get back a big chunk of health.
Can go invisible and leap at the carries in the back or use it to get away.
Is not a mana hungry champion.
Has 2 sets of abilities.

CONS

Can go down fairly quick if not paying attention.
Cool downs can be annoying early game.
Not one of the best laners early game.

MY BUILD
I get ignite for kills and flash to get away. Other viable options are ghost for chasing people down, heal for 1v1 fights, and teleport if you are soloing top.
JUNGLE
You obviously get smite for the minions. Options for you second spell can be, flash for running way or catching up to kill someone, ghost to catch up or run away, exhaust if you feel you need an extra slow to help you, or ignite to get kills
AP
I use the same spells as laning with AP Rengar because there is no big major difference between the two and spells mentioned above are viable with this build as well.
BRUISER
I use the same spells as the other laning builds. Other viable spells are heal and if you want to try it surge.

MY BUILD
While laning I get typical ADC runes, you can change it around so you are tankier if you wish. Although, I would recommend you max your battle roar first if you decide to do this.
JUNGLE
I get the same runes as laning because there is no big difference between the two. Note though that tank runes would not be very efficient in this build.
AP
These runes are completely different than the other two builds. You should get AP runes with quints and at least one other type of rune for that early extra damage. I then recommend getting some armor or MR runes for survivability.
BRUISER
Same runes as my build, you can get all armor and MR runes if you really want to be a tank.

MY BUILD
I go 21-9 mastery points making sure to get points in CDR and weapon expertise to harass early game.
JUNGLE
I go 21-9 master points but change some of the masteries so I do more damage to minions in jungle.
AP
I go 21-9 mastery points but do not take any mastery points into the AD side of the tree and only get AP mastery points.
BRUISER
I go 9-21 mastery points to be a strong tank. I get some points for AD just to have some damage while being a tank.

MY BUILD
I max savagry first while laning to give me good damage and attack speed early game, afterwards I max battle roar to give me good health back while at full ferocity, I get bola strike last because it is best used as a ganking ability rather than a laning ability.
JUNGLE
While jungling I get savagry first to get me to full ferocity so I can gank early, you should max bola strike first so you get a great slowing and rooting ability for your ganks and initiations, afterwards I max savagry to give me good burst damage against rooted or slowed enemies, finally I get battle roar for the health back.
AP
I max battle roar first because it is your primary damage dealer as AP Rengar. Then I max Savagry because even though you are not AD it is still an effective ability. I max Bola last because it does not work well with AP Rengar.
BRUISER
Same skill sequence as my build, you could max your W first if you wanted to rely on your battle roar early on. Once I get warmogs I immediately work on my battle roar and maxing it.

MY BUILD
I start out with boots and 3 health pots so I can stay in lane, if you have all the runes I suggested you should be somewhat tanky and do a lot of damage for early game and not need any other items. Instead of boots you can get cloth armor or a dorans blade. Armor if you plan to be defensive in your lane and wait for ganks from your jungler, and dorans blade if you plan to be offensive and deal out damage. After completing my boots, I move on to the bonetooth necklace for some good early AD. Afterwards, I get vampiric scepter, sometimes I get bloodthirster right afterwards, but if I cannot afford it I move onto zeal and phantom dancer and then finish bloodthirster aferwards. I then get frozen mallet which works well with battle roar. Then I get guardian angel because it gives both armor and magic resistance. If you find that the bonetooth necklace does not help you a lot, you can sell it and get an infinity edge for more damage or get something that makes you tankier such as thornmail or get warmags and increase the effectiveness of your heal even more.
JUNGLE
I get wriggles first because it gives a good amount of life steal, damage, and armor at the beginning of the game. I then get Tabi or Merc Treads depending on the enemy team. I then get bonetooth for some good early attack damage. Since I already have an item with life steal, I get zeal and phantom dancer to get a good amount of attack speed. I get phage and frozen mallet because they work well with your battle roar at full ferocity, and it makes you HP tanky. Finally, I finish with guardian angel because it is a good well-rounded armor and magic resist item. I usually sell wriggles to get something that gives me more life steal such as a bloodthirser, or I get an item that makes me tankier like thornmail. If you jungle well enough you should find that bonetooth necklace is a viable item to keep even late game with all the passives it gives.
AP
Since I have played AP Rengar only twice this is going to change often probably. I start with amplifying tone because it gives you a good amount of AP early game. I get boots so I can move with speed to chase down enemies running. I get kages lucky pick for the gold passive. I get sorcerers shoes for the magic penetration. I build Rabadans first so that I can have an extreme amount of AP early game. I grab a giants belt for later when I get my warmogs. I build kages lucky pick into deathfire because, well it is the only thing kages builds into that makes sense with Rengar. You could sell kages and get something tankier if you want. I then finish warmogs for that HP tanky feel and for the extra effectiveness of your battle roar. I grab malady for the attack speed and the AP. Then I finish with zhonyas for the armor and AP.
BRUISER
I start out with typical boots and health potions like most top champions. I then get tabi or mercery treads depending on what the enemy team has. I get bonetooth necklace for early damage. I then start working on frozen mallet. I get frozen mallet because of the damage, slow, and the health. I then get warmogs for the health as well. I then get a BF sword to do some damage. I get vampiric scepter for some survivability. I then get infinity edge and bloodthirster for my main damage items in team fights. Afterwards if I feel I have enough damage I sell my bonetooth necklace for guardian angel because it is a well rounded armor item and for the revive.

While jungling I am very aggressive, I get full ferocity at level 2 and then I usually look to gank a lane. I start with Lizards and then move to wraiths, wolves, and then golems. I usually give Blue to mid unless I need the experience. Counter jungling with Rengar is very efficient because he can wait in the bushes for his enemies and then he can take the buff at the last moment.

I hope this guide helps you do well as Rengar, tell me things I should add or take out of the build and I will change it as I see fit.
Cheers,
Bennygump

9/14/12 Fixed some spelling errors and added some more information into the guide, added an AP build.
9/24/12 Changed laning to My build and added a bruiser build.
12/14/12 Changed the mastery trees for all builds.