Tetris Attack: I've never had so much fun playing a puzzle game against someone. On top of that, that garbage your opponent sends at you can actually help you crush them!
Super Bomberman 2: My favorite Bomerman game that has multiplayer. 10 stages and tons of different powe-ups and single or team battle modes. There was a time when one of my friends didn't wanna play this game because I owned so hard at it. :P
Contra/Super C/Contra III: Bill and Lance rock hard. Your friend will understasnd if you kill him buy jumping and scrolling the screen upward to get that Spread Gun. :P
There are others but I'll post them later.