OH HO HO HO.
A warm welcome to you all. Hello. Salutations. Bonjour. Hue hue hue (for all you brazilians). I have been using mobafire for the past year, and figured it was about time I put up a guide. This is just the way that I play Kennen. Of course, I don't ALWAYS follow this same build, it's usually situational to the games I play. But for the most part, this is what I will try to build.

Let's get started.

Great Success!

Fun to Play.
Wonderful harass and quick farmer.
Incredible burst.
Can decimate a single enemy.
Able to completely change the outcome of a team fight.
Great Survivability
Able to escape ganks/chasers easily
Can stun enemies very often
He's a ninja.

Oh boy.

Runs out of energy quickly
Ultimate can only hit an enemy a maximum of three time
Usually focused first due to incredible power in teamfights.
After using all abilities, pretty much screwed until lightning rush is up again to escape from sticky situations.

You may be asking, why all the defense items? What most people don't realize about Kennen is that although he may be (arguably) one of the best AP carries in the game, he also has survivability that will help even the ballsiest of players who like to push out.
Red for Magic Pen.
Blue for Magic Resist. (You seriously have no idea how well this stacks up with items you buy. You end up with a pretty damn good amount of defense and resist.)
Yellow for health per level. (Really helps throughout the whole game. People don't expect you to have this much health, usually.)
Quints for more magic resist per level, for those pesky mid champs like LeBlanc, Kassadin, Malz, Karthus, Fizz, Ziggs, etc.

You get the picture.

Cleanse is a must on Kennen. I hardly ever see anyone use it, but people don't realize how powerful of a spell it really is. If you get CC'd, slowed when trying to go in for your ult, etc...

It will help you escape those 5 man ganks we all dread. Hell, it'll help you escape pretty much any gank possible combined with Lightning Rush. Some people say flash would be more helpful, but whats the point of that when you just get CC'd again, or chased down? (Even if you're being chased by someone really fast, remember you can kite with your skills to stun them and escape. Not that you should be putting yourself in those kinds of situations.) It's the same with Ghost. It doesn't matter how fast you are if you get locked down.

As for the Flash thing...
If you can position yourself well with teammates, you won't need it. I've tried many different summoner spells on this champion and after 30 levels of playing Kennen, I just feel Cleanse is a much better option. (Also gets ride of ignite, burns, etc. It's a lifesaver!)

IGNITE. I love this spell. If you ever feel you want that security to get a kill, or see someone about to escape your grasp, ignite is the spell for you. Works wonderfully on champs like tryndamere, leblanc, shaco, twitch, eve, talon, etc.... who have escape tools, or create clones, or go invisible.

I cannot stress how important it is to land skill shots. If you can't consistently land your Q, then definitely practice this.

This is how I usually use my skill orders. Remember to:

FARM

though, in the process of doing what I am about to write. It's important to last hit and get gold to gain an item advantage.

When lane phase begins, try and do a bit of harassing while farming. Once you hit them with a Q, try to auto-attack them and then hit your W for an electrical surge. Since you have a lot of survivability in the beginning, don't be afraid to get close. (If you over-extend, you have E to dash back to your turret. And if you get CC'd, that's where the CLEANSE comes in. It's a beautiful thing).

Wait a little bit to get your energy back up, and once it hits 100, lightning rush in for a hit again. By this point, if you timed it right, they should be stunned and you should be headed back behind your minions, with a little bit of extra energy due to going through an enemy. (You get a portion of your energy back if you pass through an enemy with lightning rush.)

Rinse and repeat.

(At about 1600 gold, I usually go back for sorcerers boots, an amplifying tomb + health pots, or all three, if I was farming well.)

Repeat the steps above again.

Once you have them to about half health, you should be still at relatively high health with the health regen, high magic resist and defense from runes and doran's shield. If people over-extend even a LITTLE bit, take the opportunity to go in with E and ult. Hit them with a Q, and ignite them immediately. Now just start auto-attacking, and watch as they try to escape with a flash, and see your auto-attacks and ignite bring them down out of sight.

If possible, help top or bot lanes. Remember to ward. Help other lanes when possible.

After you buy Zhonyas, prepare to start traveling the map with your team and ganking stragglers. Then begin pushing turrets. Don't be afraid to initiate if no one else is doing it. Remember, with the extra health and armor/magic def., you can get in, do damage, zhonyas to turn invincible, lets your team come in and start attacking, escape the heat of battle before you get killed, and turn right around to start throwing shurikens and electrical surging.

You'll be pushing towers and winning games in no time!

So, uh. Yeah. Don't jungle Kennen.
Just...don't.

Your ganks are fast, furious, and unexpected. Do gank often, and do remember to have your 5th auto attack up when you do so you can stun the enemy when you come in. :)

[2/8/20112] This isn't a complete guide yet, but let me know what you think of it so far. I'll be sure to work on it more later on this week.

[4/7/2012] Worked on it a bit more. Still trying to figure out what final build is. Will continue to work on this as often as I can, school gets in the way a lot. -_-

[11/9/2012] Woo. It's been a long time. Changed some item builds, and descriptions. Updates will come as I can work them out with S3 coming in, and taking nerfs into account.