A long-time favorite for me was Forgotten Worlds, which was like a "shmup version of Contra."
In reality, the game is not particularly good--it has flaws all over the place mostly from being a very early Genesis game, and a Sega-helmed conversion of a Capcom arcade game, but it has it's charm and my brother and I poured countless hours into it when we were kids. It also has a unique bug that gives you infinite lives--play the game in two-player and literally the only way to get a Game Over is for both players to die or be dead at the same time.