The first system I ever owned was a PS1. Bought it from a friend who bought it a year or so after release when he needed money for something else. Never had a Nintendo, although I borrowed a friend's for "a week" which turned into a couple months.
My family had an Atari, but didn't have many games for it.
After the PS1, I got a Dreamcast on the cheap, and the PS2... then a PSP, then PS3, then an Xbox 360 on the cheap a couple years ago on black Friday. Then a friend sent me a Nintendo DS as a gift in an exchange and two weeks ago my friend gave me an NES with gun controller.
Don't really need it though as I have the entire NES game catalog on a disc I can play on my Dreamcast... over 5,000 games!
So there's my history. I also have a Mortal Kombat II arcade machine.
I've also picked up cheap systems from friends etc. as back ups or for other rooms in the house... so I have
PS1 x2 (maybe 3?)
PS1 with attached screen x1
PS2 x 1
PSP x 1
PS3 x 2 (one is backward compatable, one is not)
Dreamcast x2 (one that plays burned games and one that doesn't)
Xbox 360 x2
NES x1
Nintendo DS x1
I think that's it. And I have a crap ton of games. Need more time to play them!