PS1 is the first console I can remember having. That had Crash Bandicoot 1, and Spyro the Dragon
SNES was next, in fact I still have my original. It was my mum's collection. Still have our original copies of SMW, Earthworm Jim 2, Stunt FX Race, Mario All-Stars, and a few lesser known titles.
Next would probably be the original XBOX. We got nearly 20 games with it at a yard sale. Grabbed by the Ghoulies, Tony Hawk's Underground 2, Bloodwake, Crimson Skies, Scaler, and more.
Genesis came next, because when I was 7 I saw it at a yard sale and thought it would play my Game Gear copy of The Terminator. Parents, said no as they wanted $20(which at the time even, was a god deal), and the lady gave it to us for free. Realized it didn't play game gear games, so I got MK3, and until 2 years ago it was my only genesis game.
Got a GBA for my birthday with Pokemon Emerald.
After that point I was old enough to get a job, started to buy my own stuff. First console I bought myself was a PS2 Slim, still have it along with the "Mortal Kombat Kollection" I bought with it.
Built up other collections until I got my Game Gear with Talespin.
Next was a flea market Game Boy Pocket, came with Tetris
Then I bought an Oddyssey 2, I got Keyboard Creations for it, I now have 7 games
PS3, first game Heavy Rain.
Wii, New Super Mario Bros or DK Country Returns.
Took me forever to get an NES, but I got one and the first thing I bought was a CIB SMB3 and CIB Dragon Warrior, loose Dr. Mario, SMB/duck Hunt/ Track Meet, and SMB2
DSI a friend gave me when he got a 3DS, no games with it, bought myself Golden Sun Dark Dawn
N64, came with Scooby Doo Creepy Capers
2600, Jungle Hunt, I think?
I believe that is it.