Atari 7800 - I don't remember.
NES - came with Mario/Duck Hunt got it and Zelda one year for Christmas.
TurboGrafx 16 - Only had Keith Courage that came with it.
Genesis - Came with Sonic I think Taz-Mania was the first game I got.
SNES - Came with Mario World I think I got the system, Final Fight and X-Men: Mutant Apocalypse one year for Christmas.
PlayStation- I got the system, Ridge Racer, Battle Arena Toshinden and Killing Zone one year for Christmas.
PS2 - I can't remember. I remember buying it paying cash and $50-$60 worth of quarters and had to wait a month or 2 after that to afford a game.
PS3 - Assassins Creed III and Mortal Kombat Komplete Edition all bought the same day.
Game Boy - came with Tetris I think I got it, Super Mario Land, Mario Baseball and Teenage Mutant Turtles: Fall of the Foot Clan one year for Christmas.
Game Boy Advance - Bought it and Advance Wars, Doom, Wolfenstein 3d and Super Mario World all the same day on Ebay.
PC - First game I picked out from a store was Double Dragon.