Akali is a squishy/carry destroyer with amazing burst. She is surprisingly versatile, so there are a lot of different ways to build her. I've seen and played a lot of builds, and this is what I think works best. Please note that this is more of a 5v5 build, and I wouldn't advise playing this kind of build in a 3v3.

Pros:
Amazing burster
Amazing chaser
Gank suvivability
She's a ****ing ninja. Nuff said.

Cons:
Squishy
Countered by oracle
Difficult to master.

I go Magic Pen marks (for obvious reasons.)
health seals (for survivability.)
and AP glyphs and quints (to activate your passive + more DPS.)

When you first start out, grab a Doran's Blade and a Health Potion. As of 3/15/11, Doran's Blade now has 10 damage and activates your passive with defensive masteries, so that's the best choice. Some might think boots are best to get first, however, at this point in the game you shouldn't be overextending too much and shouldn't have to worry about ganks. However, feel free to grab boots before you get Hextech Revolver if you wish. Farm until you have at least 1200g or you die, then go back and grab a Hextech Revolver. Next, grab your Boots of Swiftness. I prefer these boots because you're a chaser, and should be able that extra speed to catch your prey. Before you get anything else needed for Rylai's Crystal Scepter, grab a Giant's Belt. The health you get from it will give you that extra boost of survivability you need. Pick up Rylai's afterwards. Next, grab your Rabadon's Deathcap, and after that, get your Lich Bane. If the game is still carrying on, upgrade to Hextech Gunblade.

The last item (in place of the Doran's Blade), as customary for most builds, is up to you.

Some items I suggest:
Zhonya's Hourglass- A nice healthy boost to your AP, and that armor is good against AD champs.
Force of Nature- Great survivability against HEAVY AP champs.
Randuin's Omen- Great when facing HEAVY AD teams.
Frozen Mallet- A nice increase in health, and the slow is good too. An all-around useful item.
The Black Cleaver- A decent DPS boost. Great for if the other team is (armor) tank heavy.

I go 21/9/0. In the end, late game survivability is EVERYTHING. The DPS increase from 21/9/0 is nice, but it won't get you far if you're dead.

I take Flash and Exhaust. It gives me the perfect mix of chasing potential and getaway potential. Teleport is also a good choice, but I think Flash and Exhaust are the way to go.

Good Laning Partners:
In my experience, I've had good progress with Morgana, Fiddlesticks, Jarvan, Garen, Soraka, Xin Zhao, Maokai, and Veiger.

Chasing:
As a chaser, there is generally a formula you should follow:
Mark of the Assassin ==> Shadow Dance ==> Auto Hit ==> Crescent Slash ==> Mark of the Assassin ==> Shadow Dance.

Use Twilight Shroud with your best judgement.

Rinse Wash Repeat.

Early game:
From level 1-5, stay conservative. Don't overextend, and make sure to stay relatively close to your turret after the initial gank at the beginning of the game.

At level 6, it's time to have fun.

Mid game:
It's your time to shine. You can pretty much destroy squishies with half-3/4th health that aren't turret hugging. Help your team out around the map, and gank where needed.

Late game:
At this point, (approximately lvl 12-18) others will inevitably start to be getting stronger. Make wise judgements, attack with an exit strategy in mind, and use your Twilight Shroud and summoner spells WISELY. In team fights, drop your Shroud in the the middle of the fight, and target the squishies and carries.

I hope you enjoyed my guide. Please rate and comment, I look forward to hearing your criticism and praises. (Hopefully mostly praises.) Try my guide out, see how it does, and let me know! Thanks for reading.

-Stropko (Find me on LoL! We'll do a 5v5 and show you how it's done :D)

3/10/11- changed rotation. (Thanks Aether!)
3/15/11- Fixed to accommodated new Doran's Blade stats