Outlaws (1985)

In Outlaws you play a wild west hero called Lone Rider. The game takes place on the prairie, and in cities. It's a side-scroller, and you sit on the back of your horse during the entire game. The enemies in the game are mostly bandits, but occasionally Indians will attack you as well. You can ride in both directions, fire at enemies with your handgun, and jump over obstacles with the horse. To avoid being shot, you can also duck in the saddle.