I began falling out of gaming somewhat in the PS2/GCN/Xbox generation. I hung onto my Dreamcast and played that regularly through part of 2004, and I didn't have such a deep appreciation for many games on the consoles after the DC. I do still have amazing favorites from that generation, though. MGS2/3, Outrun 2006, etc.
I guess I was playing more of my PS3/360 consoles, but very little has really stuck for me. My 360 pretty much became my Guitar Hero/Rock Band console. My PS3 only sticks around for Metal Gears and its media capabilities. I got the Wii late in its life, but I'm actually kind of excited to pick up some of the games I missed. I picked up Excitetruck a few weeks ago, and I enjoyed it.
So, with the lack of games and all of the 360 consoles I went through, I guess that generation is my least favorite.
It wasn't until I built my PC in late 2009 that I began getting into gaming again. I do have some PC versions of popular console games from the PS3/360 era that I love, though. Sega Rally Revo, Stranglehold, Star Wars Force Unleashed, Metal Gear Rising, Sonic Generations, Binary Domain, and others.