Pros:

1. Tanky, you will be pretty hard to kill.
2. Great item/skill synergy for team fights.
3. Great Laning power.
4. Decent dmg output.

Cons:

1. Not as much AP as some other builds.

I've been playing Kennen for a while,and he has always been one of my favorite champions. There aren't too many ways to play him, mostly you're concerned with Maintaining high dmg output and CCing. This build will take a slightly less conventional approach. I'll be focusing on maximizing your survivability, while still keeping dmg output at a threatening level.
The mindset you should be in while trying out this build is:
"Okay... "I'm just gonna jump in there and mess up the place." *dust clears...enemies are dead*

These are your standard AP caster Runes and Masteries.

Marks
Greater Mark of Magic Penetration are fantastic and will give you high dmg against any champ until they start getting MR.

Seals
Greater Seal of Scaling Ability Poweris a great way to keep your AP up for late game. Feel welcome to switch these out for movement or attack speed or whatever your play style demands

Glyphs
Greater Glyph of Ability Power really help you boost your early game lane dominance.

Quints
Greater Quintessence of Ability Power also are a great way to increase your early dmg and get First blood.

For Masteries I take every stat that will help me deal more damage through the game. This is nice since we are building rather tanky items, the masteries give you that extra ummph to stay threatening. Fill out some masteries in utility for extra movement and flash cdr.

First starters pick up Boots of Speed and Health Potion x2. This will help you dodge skill shots and retain laning power. This should last you until at least 4-5, but you can probably last longer than that. If you don't think you need the extra speed at this point, and are confident with only 1 Health Potion, then grab an Amplifying Tome here.

You'll want to head back and pick up the . This will eliminate your need for health potions. This and boots will be your core for early game. Also buy a ward or two if you can.

Depending on if you have gotten some kills and some good farm, you'll want go straight to , this is the core item of the build and playstyle. The hourglass enables you to flash or rush into fights, pop your ulti coupled with hourglass soon after and watch the fireworks. This tactic will be described in greater detail later in the guide.

Make sure you pick up your pretty soon to add to your mobility and stare resists. They will help in late game for more tankiness.

Go back and pick up a . This will add to you Spell Vamp and give you even greater laning power. Using the E+W farming combo will give you a huge chunk of your health back, and your Q will also give a good amount as well.

Next up is priority based between / and . This is based on how the enemy team is doing, if they have an AP or AD carry, and what your stat needs are.

should be your choice if the enemy has a strong AD carry, it will give you 400 HP and 45 armor, making you that much tankier. It also synergizes with the ulti+zhonya combo nicely. Additionally, you could choose in this place. You'll have less armor this route, but more AP and more damage overall. This is a preferential choice. You'll be slightly less tanky, but more threatening.

is your best bet if they have a strong AP carry giving you 70 AP, and 57 magic resist. It's aura also synergizes with your main combo by lowering the Magic Resist level of nearby enemy champions by 20, making your skills hurt that much more.

Which ever item you didn't take in the last step, get it now.

Last you can grab a which will greatly increase your dmg output. At this point you will be a healthy, armor stacked, magic resist, AP carry that can take their team down and out. This could also be a good place to put in , making you even MORE tanky, but less DMG output overall. Again, a preferential addition.

Mark of the Storm
This puts a mark on the enemy that when it stacks to over three, the next strike will stun the enemy. This is applied by any of your skills. So basically if you use all three of your skills on one enemy, they will be stunned. This is what makes Kennen so great/annoying.

Thundering Shuriken
This is your main farm and harass spell. It deals some great damage early game, and can take chucks out of your opponents health bar. It has a really low cooldown and since you are an energy based champion, spam it as much as you can.

Electrical Surge
Pick this up second, and max it out second. This is another great way to harass the enemy champion once they have an orb on them. Also, this enables your fourth auto attack to charge up and deal extra lightning dmg which also procs your passive. Many new Kennens will ignore this passive, but mastering it will set you apart as one of the best.

Lightning Rush
Turns you into a ball of lightning, increasing your movement speed and causing any enemy you come in contact with to receive lightning dmg, activating your passive. This is a great chase/escape mechanism and can also be used in coupling with Electrical Surge to clear waves and waves of minions generating farm quickly and efficiently.

Slicing Maelstrom
This is your big bomb, your super nova, your megaladon. Pop this baby in a team fight and seem the enemy team get destroyed. In coupling with your Lightning Rush and Electrical Surge this will stun their entire team and do awesome dmg while the rest of your team nukes them down. Before the enemy even realizes what happened, it'll be too late.

You'll want to Mid or Top lane, this is where you will crush the enemy. I have never been unsuccessful 1 vs. 1 as Kennen. The only time you will have a problem is if you over extend and get ganked by the enemy jungler. Otherwise, if you keep your harass up, your opponent will be too low to jump you, and eventually you can get the kill.

Solo Laning:
Last hitting minions is number one. Use your auto attacks to do this if you can, and your Thundering Shuriken to clean up any out of reach creeps. If there is an opening, try to land some harass on the enemy as much as possible, not only will this help you get first blood, but will also scare them out of getting farmed.
Use the E+W combo to farm up minions quickly (only do this if they are near your turret and you know the enemy won't jump you as this will make you slightly more vulnerable)
Ward local bushes as often as you can in order to avoid ganks.
Once your lane is pretty well pushed, and you have some of you core items, you can start ganking bottom.

Ganking:
Try to come in from behind while the enemy is extended. Tap them with your Lightning Rush then pop Slicing Maelstrom next use Electrical Surge and they enemy will be stunned. Follow up with a few [Thundering Shuriken and Ignite if you need. Don't be afraid to Flash into range or around creeps or champs to land that last Thundering Shuriken to get the kill.

Getting Ganked: If you see a gank coming in on you, Lightning Rush away, and Flash if you need to. If you're pretty well farmed and your lane opponent is low, you might be able to pick up the kill by turning the tide, dropping Slicing Maelstrom and then turning on their jungler/running away depending on your health.

Flash
This is the best summoner spell you can possibly have, it gives you great ganking ability and really works well with the team fight combo of Flash+E+R+W
Ignite
The best for 1 vs. 1 in lane, this will get you first blood.

Other options:
Ghost
Also helps with ganking and getting into or out of fights. This with Lightning Rush Can really close the gap.
That's it, everything else doesn't really help with this specific play style.

Okay, I've mention this a few times in the guide so I figured I should go into greater detail here:

Position:
Get into a good ganking position. This is where being a ninja really comes in handy. Get in a bush where you can zoom out, or behind a wall that you can flash over. This is the preferred position to be in because it keeps you from being silenced or CC'd before you can get your whole combo off. If the enemy stops you from blasting your ultimate you basically wasted your ambush.

Combo:
Flash* + Lightning Rush + Slicing Maelstrom + Zhonya's Hourglass + Electrical Surge = They're dead.

Note:You may need to move the position of Electrical Surge to before the Slicing Maelstrom for the extra nuking power. I like to use it after as it will help proc another stun sometimes. However, using it before the ulti ensures that those closest to you will be stunned, adding a greater strategy component, and also ensuring that they will have a mark from your passive on them.

Why you have your items:
All the items in this build are intended to maximize this one combo. That's not all their good for, but its what they do best.
Mercury Treads Keep you from getting CC'd too long. And add to you MR
Sunfire Aegis Makes you that much tankier through HP and armor, and it's passive adds to you AOE dmg.
Abyssal Mask Also increases the amount dmg you put out and gives you a lot of MR
Rabadon's Deathcap Keeps your AP from being too low to be threatening
Zhonya's Hourglass gives you armor, AP, and its Activation will allow you to come out of the fight without a scratch.

Now you may be asking, "Why so tanky is the hourglass keeps you from taking damage". The answer is simple. Let's say your the initiator on your team, using your Ultimate Combo to start the team fight. Now, let's say you get silenced and you're NOT tanky... Well then you can't do your combo, and you're dead almost instantly. By being tanking, you can last just that much longer to get through any CC they enemy might through at you, and then still pull off your combo, albeit a little late. It also keeps you from being the main target like most squishy AP casters.

This is my personal favorite way to build Kennen. It yields a lot of survivability which means more forgiveness. I recommend this build if your new to Kennen, or are a casual player. I'm not sure how viable it is in ranked games, but I'm sure it has its uses there as well. Good luck and please leave comments below if you have any question/concerns about the guide.