I went N64.
I had been in college and largely broke during the SNES days, so I missed an entire generation of gaming (thanks Virtual Console!), but I had an NES so I was a bit predisposed to Nintendo anyway.
When the N64 was preparing for launch, the PS1 had a pretty shitty catalogue (big, but shitty) and I hated the controller, so I wasn't really interested. As a SF nerd, I was wowed by what I saw of Shadows of the Empire (the Hoth level) at conventions, and the Mario 64 kiosks at TRU had me hooked.
I eventually got the N64 after the XMas launch (waited until after the holidays as I figured there was a better chance of it going to a kid then- this was before eBay drove the speculator market into overdrive) along with SM64 and SoE, and never regretted it (thankfully SoE was the first game I played, so I was too wowed by the "2 gens ahead of where I left off" factor, and didn't notice how shitty it could be - esp the controls - until I had a few more games under my belt).
I was just out of college, had no significant other, and a job, so I had money and time to spare. I was able to play games to death in a way I am no longer able. I can't say I completed all of them (like many of the platinum medals from Blast Corps), but I was pretty thorough, and to this day many of the N64s games remain among my fondest memories. Most notably:
Banjo Kazooie
Mario 64
GoldenEye
Perfect Dark
Blast Corps
Mario Kart 64
Diddy Kong Racing
Wave Race
1080
Snowboard Kids (deceptively fun title)
Turok 1 and 2
All Star Baseball
WWF Raw
Doom 64
Duke Nukem 64
Conker
EDIT: $^&! How could I forget Ocarina!
