Touhou is a pretty fun game. That is if you 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 you can find online.
Playdom.com has alot of cool games. Alot of their games are strategic in a sense but you don't need to be a genius to play.
This is Touhou (video) in case you were interested.
You could also try looking up "flash games" and it should give you plenty of results.
