My favorite game is Contra Hardcorps. It's run n gun for Genesis.
There are other games in Contra series before and after this one but this one is the best cause it features 4 heroes each with different set of weapons.
I love the challenges presented by the game and the boss fights are great! Even better, the game has 4 different main paths which leads to total of 4 different endings. Well, actually there are 6 endings in total, but one of them is joke ending while the other is bad ending.