So, this is my favorite console of all-time. My parents totally surprised me with one for Christmas in 2003. This was THE console in our college dorms and later in our apartments. There are two games that I played over LAN with friends that gave me tons of timeless memories - Halo: CE and Sid Meier's Alpha Centauri.
For me, this was a quasi-continuation of the Dreamcast, which was my favorite console ever at the time, so I spent a ton of time with JSRF. I remember being so excited for Panzer Dragoon Orta and getting it on release. I also could list a ton of local co-op and competitive games that were incredibly fun: NFL 2K5, Deathrow, Gladius, Kung Fu Chaos, Halo: CE and Halo 2, FIFA and NFL Street, SEGA Soccer Slam, Links, Top Spin, Blitz: The League, and so forth. When I was at home for summers a couple of times before I got my own apartment, I would spend time with my siblings playing Fuzion Frenzy, a game that I will defend to the death.
I fucking love this console's game line-up, and I didn't even get into the great single-player experiences that I had with it (KotOR 1 and 2, Buffy the Vampire Slayer, Indiana Jones and the Emperor's Tomb, Spider-Man 2, GunValkyrie, Def Jam: FFNY's amazing single-player mode, Jade Empire, XIII, Crimson Skies, GTA: San Andreas, Brothers in Arms: Road to Hill 30, etc.)
My console, which needs a disc drive/optical laser replacement really badly, has a bunch of music that I put on the hard drive that basically are memories of my life for about five years.
Like I said, this is easily my favorite console ever, and probably, it's never going to be surpassed.