Here goes mine in approximate chronological order:
1) Pong = Okay so it wasn't quite the first, but it's close enough for me.
2) Space Invaders = The original shoot-em-up
3) Pacman = The first cult game character
4) Elite = Exploration? Comnbat? Trading? All there and has yet to be bettered IMHO
5) Outrun = This is what I'll be spending my pennies on in an arcade
6) Tetris = Defined the puzzle genre thanks to it's simplicity and availability on many platforms
7) Xenon II = Proved games could be cool thanks to the admittedly tenuous Bomb the Bass tie-in
Shadow of the Beast = Set a precident for eye/ear candy over content. Sold many Amigas!
9) Mortal Kombat/Street Fighter = Defined the term "Special Move"
10) Wolfenstein = Original FPS
11) Tekken = Took the beat-em-up genre to a new level
12) Gran Turismo = Inspired thousands to buy Vauxhall Novas (old Opel Corsas) and fit howitzer sized exhausts