Streets of Rage deserves a mention, as it is truly awesome. Also, thanks for this, I'll probably download some more games now I know what to avoid.
Edit: Downloaded BATTLE LODE RUNNER and Bomberman '93 yesterday, Bomberman is a bit repetitive on single player but still a lot of fun if you have two or more players. BATTLE LODE RUNNER is a lot more tactical than it first seems, and you have to actually figure out the way to do a level as well as avoiding the monsters. It's not a truly brilliant game, but its worth a look if you like action/puzzlers.
Edit: Downloaded BATTLE LODE RUNNER and Bomberman '93 yesterday, Bomberman is a bit repetitive on single player but still a lot of fun if you have two or more players. BATTLE LODE RUNNER is a lot more tactical than it first seems, and you have to actually figure out the way to do a level as well as avoiding the monsters. It's not a truly brilliant game, but its worth a look if you like action/puzzlers.