Warning: This build takes a lot of skill and teamwork. If you feel you can't rely on snowballing, this build is not for you

Intro: Kassadin is a great ganker with a low cooldown ultimate which is great for initiating ganks, therefore Kassadin deserves to have his place in mid lane.

Early Game: Start with Meki Pendant for early mana regen and two health pots to keep you in lane as long as possible. Harass the enemy with Null Sphere as often as possible without using up your mana completely. If you can zone him, do so without putting yourself in danger of ganks by staying map aware, or only last hitting minions with auto attack. By auto-attacking, you put yourself at great risk, but getting your ult asap is the most important part of this build. The most important part of early game is that you nuke your opponent so they die before you do, giving you three or four free farms.

If they rush you, Ignite them right away to gain your additional 10 AP, Heal, then R > E > Auto-attack > Q (if necessary). If done correctly, this should ensure you a free first kill.

Once you farm enough for a tear and a boot, go back to town, and continue farming until Amplifying Tome, or even Mejai's Soulstealer.

Mid Game: Always be map aware. With your Soulstealer, grab as many kills and assists as you can, and once you have enough gold for Sheen, return to town and grab it. Farm, gank, help your team, whatever it is you think you should be doing, do it, but remember DO NOT DIE! losing stacks is the last thing you need. Buy Leviathan, and continue stacking.

If you or your opponents haven't already surrendered, the real fun starts.

Late Game: Once you get your snowballs rolling, never let yourself be set back. Use Heal for baiting, and baiting ONLY! Grab Lich Bane whenever you can to increase your auto-attacks' damage (this is especially helpful in taking down towers). Learn to synergize your Force Pulse with Lich Bane and auto-attack. Be the last one in and out of team fights, and remember to NOT DIE!

In a team fight, use Null Sphere whenever possible but stay out of the fray until one or two of your allies or enemies have gone down, then R in and unload, focusing your skills on the squishiest targets and auto-attacking beefier champs with your auto, but remember to only use your R again to either escape, or finish off. It is a last resort skill in a team fight unless you're absolutely certain they're going down with one more hit.

Finish Archangel's Staff and Deathcap, and you'll have enough AP to 3 or 4 hit a turret with Lich Lane proc'd.

Summary: Farm (without dying), bait (without dying), and kill (again, without dying) as much as possible. Be sure to keep your snowball rolling, and never let yourself be caught alone with a cc heavy opponent. Stuns/roots are your worst nightmare, and because you dont have cleanse, heal is the only thing that can save you in a pinch.

Remarks
I started using this build after being completely ROFLstomped by the craziest Kassadin player i've ever played against, although my build is slightly different. i spent the whole game chasing him and he baited me. every single time i thought i had him, i was met with a null sphere to the face and a "BLARGHH", and sure enough, i was dead, and his heal had saved him. i hope this build will serve you as well as it has served me. good luck, and remember:

silencing your mother = a big no-no