Why is Kassadin not played very often in high-level competitive play? In casual play he is an almost constant ban, but not in the big tournaments streamed online as part of Season 2, such as the ggChronicle going on at the moment.
He is actually very easily countered, as he specializes in countering standard mid mages, you just need to pick less common things to counter him, which does not happen as much in solo queue.
For instance, Fizz, Talon or any AD carry all counter him quite easily and make his laning phase quite miserable.
And if he gets behind, he needs to roam to get kills, and organized teams are a lot better at avoiding random jumps from him, due to warding, enhanced map awareness and better communication.
So essentially, it is too complicated to get ahead with him in a tournament and isn't worth the risk.
The thing about kass is that he eats up mana, and is a snowball champ. That means is weak at first but then spirals into power, but the weak early game is a huge problem for him. If kass doesn't get any kills he doesn't do very well, but he tends to pick off champions by ulting through walls quickly.
He isn't played much in ranked because ranked games are all about how team works together. Annie, cass, ryze, malz, all have abilites that have cc, high damage, and aoe which works well with groups. Kass has a small AOE, which requires getting close.
TL:DR? Doesn't fit well in team fights compared to other ap because of high cool downs.
Kassadin actually does show up in both tournament play and high level soloqueue. The reason you don't see him is because you aren't watching the right players. The Rain Man, formerly, of TSM, plays quite a bit of Kassadin in solo queue (If you'd like to watch some of his gameplay as Kassadin, you can refer to his Kassadin guide on Solomid.net). As far as tournament play, Kassadin typically shows up more frequently on European teams. Ocelote of SK and Froggen of CLG.EU both play Kassadin, though his primary function is as a counterpick, which makes it risky to pick him any time before the opposing team has selected the champion he will lane against.
Rumble vs Kassadin is also quite amusing. Any champion who can put out DPS while silenced can counter Kass.