Since most of my mainstays (Sonic, Ristar, Streets of Rage, Thunder Force series) have been brought up, I'm gonna try to go for a few games no one's mentioned yet:
Cyborg Justice: A never-named game from my childhood. It's been a while, maybe it doesn't hold up as well as I remember, but it's an interesting premise. It's a 2D beat 'em up where you play robots. You build a custom bot for yourself at the beginning of the game, which changes up your attacks/appearance. Here's the kicker: maybe you run into an enemy bot with the flamethrower arm, & you regret taking the chainsaw arm. So- steal his! You can literally rip apart any baddie you go up against & take their parts as your own. Be careful, though- they can do it to you too!
Sparkster: A couple folks brought up Rocket Knight Adventures, so I'm surprised no one's mentioned its awesome sequel!
Landstalker: An isometric action RPG that's great fun for fans of old-school Zelda. Just, um, make sure your can save. I lost a lot of progress to a dead battery once.
Since Aladdin's been mentioned a few times: if you get stuck, pause & quickly hit a,b,b,a,a,b,b,a. Do it right & you'll auto-complete the level. I once beat the game at Disneyland doing that.
