Touhou is a pretty fun game. That is if anda don't mind an Anime style game. And it's somewhat of a dodging strategy game to honest. But there are some Touhou fighting games.
There's like I think 19 official Touhou games and alot of unofficial ones.
There's also sonic the hedgehog flash games anda can find online.
Playdom.com has alot of cool games. Alot of their games are strategic in a sense but anda don't need to be a genius to play.
This is Touhou (video) in case anda were interested.
anda could also try looking up "flash games" and it should give anda plenty of results.