Atari 2600 - My parents bought it for me from Florida when it still wasn't available in Canada. Aside from the Combat pack-in they also bought me Pac-Man (sooo bad, but loved it at the time)
Colecovision - Parents won it at a raffle, came with Donkey Kong, I quickly begged them to buy me Zaxxon separately.
Commodore 64 - First game was a budget Mastertronic game called 'Hero of the Golden Talisman'. I distinctly remember picking out from behind a glass case at Zellers
PC - Commander Keen, shareware edition
NES - Was late to the NES because I believe consoles were stupid after the first console crash. Finally caved when Super Mario Bros 2 came out. Bought it with the system.
Gameboy (B&W) - Got one for X-mas. Parents got me Super Mario Land to go with the Tetris pack-in.
Genesis - Sold every NES game I owned to come up with the cash to buy the Genesis and one extra game when it came out. Extra game was Space Harrier 2
SNES - Couldn't wait for the North American release so I sold all my Genesis games / system to come up with the cash to import a Super Famicom with some games (no pack-in). Cost me (as a 15 / 16 year old a fortune at the time)
I bought Super Mario World, Gradius 3 and Big Run
PSX - Bought the system, Ridge Racer, and Battle Arena Toshinden the same evening.
N64 - I dont remember if Super MArio 64 came with the system or not but I had that and Pilotwings 64
Dreamcast - Just bought the system and Soul Calibur
PS2 - Imported Japanese version with Ridge Racer 5 and Street Fighter EX 3
Gameboy Advance - Imported Japanese version with Castlevania Circle of the Moon & Super Mario Advance
Gamecube - Preordered from Best Buy with Wave Race Blue Storm and Rogue Squadron 2
Xbox - Unit + Halo
PSP - Bought at launch with Ridge Racer and Darkstalkers
Xbox 360 - Bought at launch with Perfect Dark Zero
PS3 - Didn't buy until much later, from the classifieds with Uncharted
WII - Got one for Xmas the year it launched with Excite Truck and Super Monkey Ball Banana Blitz