Double Dragon
Street Fighter II
Diablo I (now you have 20000 clones of it, even Vampire Redemption)
Starcraft (ok, it's modern but I think that it was the first time the different razes you could choose were truely different... in other games like dune2 or warcraft2 the razes were too similar and played almost the same...)
Pang
Dungeon Master
Super Mario Bros
Monkey Island (it wasn't the first, but I think that graphic adventures became quite popular thanks to this game)
Quake3 (ego shooter but with only deathmatch)
Tomb Raider (I guess Max Payne wouldn't be here without it)
I would say Half-Life, but I would put it in the Wolf3D genre...
Sim City