Not Updated For Current Season
Since Kassadin's Riftwalk can stack and his Force Pulse needs to charge, I like to think of him as a snowball champ. He is very item-dependent and will need lots of AP, which is why you're gonna buy a Mejai's Soulstealer and Rod of Ages. This basically means if you suck *** early game, you will suck major *** later on. Be very cautious early game.
Kassadin was made to counter mages, just like Jax was made to counter DPS. His Riftwalk allows you to move over the rough teamfight and reach the squishy ones in the back. The silence ball will render them useless for up to 3 seconds, giving you plenty of time to poop on their face. The basic combo is: Riftwalk in > Force Pulse > Null Sphere finish them off (not too hard, just a couple of auto attacks and Ignite) > then Riftwalk out.
A good team will pick up your tactics real quick and will aim their fire at you as soon as you pop out, especially if you have stacks on your Mejai's Soulstealer. So when the team fight breaks out, wait for some sparks to fly, then **** on the casters. Also, you won't have to worry about not having enough stacks for your Force Pulse. In teamfights, 20 abilities will fly over your head, so your only limit is the 5 second cooldown.
As an anti-caster, you're going to be dealing with a lot of spells in your face. This is the reason for packing magic resist. This will leave you vulnerable to heavy DPS (pretty much your only weakness). But, that doesn't mean you're useless against them. You still have TONS of burst with very short cooldowns and an escape mechanism.
This is my version of SimplyBuklau's build over at leaguecraft. It's modified for a little more magic penetration and AP. The said above is a quote from him.
Changes I made to his build: Added Void Staff for MP; remade masteries; changed Clarity to Heal;
Here is a Kassadin gank potential demo from SimplyBuklau:
Notes: Be sure to buy Elixir of Brilliance whenever you have a little gold left. At the start, when you buy Meki Pendant / Sapphire Crystal you should also get 1 Health Potion and 1 Mana Potion. Do not be greedy and do not steal from your teammates (everyone knows how annoying that is).