Rapid Reload is one of my favorite run n' gun games. It's an old obscure PS1 game that was only released in Europe and Japan.... so unless you're keen on importing games, the only way to play it is to use an emulator, but even so, it's awesome!
If it's limited to 2D games I'm pretty much outta here, but if it's NOT then I'll stay. Beyond the usual suspects of Doom 1 and 2 and the first Quake games, Painkiller is one of the best 'classic' styled ego-perspective-shoot-em-ups that exists. great weapon- and enemy-design, really cool leveldesign and a goddamn great gameplay.
i wouldn't call contra a run n' gun as you call it. i tried that in the original contra and i died very quickly. is this only limited to 2d games? if so then metal slug really is one of the only ones that come to mind. however megaman zero 4 i think it was came pretty close when you had weapons fully upgraded. alot of the areas i could run n'gun.
if 3d games count to then id have to add the original quake games to that list and the unreal tournament games.