this game introduced mario aka jump man. Although it may not be the first platformer, it was the most enduring.
Galaga (arcade)
Not the first shoot em up, but the one that stepped up the graphics and gameplay of space invaders, asteroids and defender.
Pac Man / Centipede
Both were the first video games to have a large female player base.
Street Fighter 2
This game popularized fighting games. Although I am not a huge fan of the street fighter series (I was more of a Mortal Kombat guy) I gotta give props to the one that ripped the door down.
Phantasy Star Online
Not for gameplay, not for graphics, just for the fact that its the first console based game that had internet multiplayer AND was massively popular. The first nail in the coffin of the arcade.
These are the games I feel are the most influential. Not the first usually, but the most enduring. The games that popularized genres. Do you want my bad taste in games? The games I have sunk serious time into?
Castlevania NES
Nobunga's Ambition NES
Metal Gear Solid PS1
NFL 2K (YOU HAD TO BE THERE TO KNOW HOW STINKIN' AWESOME THIS GAME WAS AT LAUNCH)
Arkham Asylum PS3
