Atari 2600 - 1982 couple of years after launch

Gameboy - One year after launch

N64 - At launch

Gamecube - 2 months after launch

Dreamcast - One year after launch

Xbox - Never owned, borrowed a mates to play Halo

PS2 - Seven years after launch

X360 - Year after launch

Wii - Six months after launch

PS3 - Not yet owned but will buy when price hits 200 GBP or killer app is released

My usual criteria is based on price and titles available that appeal to me.

The 360 was bought primarily because I wanted to play Dead Rising and Bioshock. 

The Wii had a unique selling point in the Wiimote and a very sweet price. 

SNES - US launch
Nintendo 64 - circa 1998
Game Boy COLOR - US launch
Game Boy Advance - US launch
Gamecube - Day before US launch
Wii - March 2007

Yeah, I was a bit late with Wii, but a lot less than N64 :P

SNES - AUS LAUNCH
SONY PS1- AUS LAUNCH
N64- AUS LAUNCH
GAMCUBE - AUS LAUNCH
XBOX - 3 months into generation
PS2 - AUS LAUNCH
PSP - AUS launch (Sold 6 months later)
PS3 - AUS LAUNCH - (Sold 4 weeks later :#)
XBOX 360 elite - AUS launch
Dreamcast - AUS launch

SEGA megadrive - launch

Atari - about 12 years after launch (lol)

Wii - one year after launch
As you can see i like to buy things when they come out Lol.

I learned never to do that again after the ps3

Atari 2600 - xmas present "couple" of years after launch. (xmas 1983)
NES - xmas present 2nd year (xmas 1986)
Genesis - won in raffle at Sears (summer 1993)
SNES - obtained myself by returning Genesis to different store during 2nd year (summer 1993)
N64 - purchased myself a month or so after launch.
GC - bought 2nd hand off a friend, during my final year at University. Would have gotten it earlier but, had to ensure I would not be distracted while at school. (fall 2004)
Wii - February 15, 2007. 3 months after launch.