When people think of classic run and gun games, the first thing that usually comes to mind is Contra.  But anyone who has played Gunstar Heroes knows that it's possibly the best run and gun ever made for the home console.  It's intense, the action never stops and it impliments some unique gameplay elements that make the game a lot of fun to play.  Also, unlike Contra, the game isn't insanely hard, but has a really balanced difficulty level.  Nintendo was gracious enough to put this on the Virtual Console, so even if you don't have a Genesis, you can still download it for 800 Wii points (eight bucks), and you don't need a Classic Controller to play it.