AP Kai'Sa
With her AP scalings (especially on upgraded Q), I think that Kai'Sa could make for a pretty fun AP burst mage, but there is a sliiight problem with this. Namely, the best ability for AP Kai'Sa, her Q, can only be upgraded by building bonus AD, which is very frustrating if I'm going to build AP. I could build, say, 3 gunblades, 3 rageblades, or perhaps a combination of both, but that's generally a pretty terrible idea. Personally, I wish there were a way to unlock the Q's potential when I'm building AP. For example, let it unlock when she reaches 40% cdr.

(not that exact order). You are incredibly squishy, which could be a problem, but you have 40% CDR, all evolved abilities, and amazing burst and wave clear.