The PS2/GC generation, as a whole, to me, was a time where I just kind of fell out of gaming. I didn't STOP playing games, but I didn't buy myself a new console until late into the gen, and just grew kind of disinterested with the direction gaming was going in general. Arcades were fading out, something that had been huge to me since the 80s. PC games were starting to become more like console games, or were just becoming straight up ports of console games. Games were becoming more about being a "cinematic experience" over a gameplay experience (something that has sadly carried on and evolved), etc.
My "company of choice", if I have to have one, is Nintendo. I grew up with the NES, and Super Mario Bros. is the game that made my really love gaming. But I certainly haven't loved EVERY game they've ever put out, and that was driven home even moreso on the GC. I think the GC was a good system, overall. But it was similar to Dreamcast in the respect that Nintendo seemed to experiment with a lot of odd ideas, "fixing what ain't broke", so to speak, and I just didn't care for some of the results. Mario Sunshine, Wind Waker, Double Dash, and especially Star Fox Assault, I simply didn't care for (the last one actually being more like: "fucking hated").
And in general, there are just games/series that I have never really gotten into, like: Pokemon, Fire Emblem, Mother/Earthbound, Brain Training, Professor Layton, most of the Wii ____ games (though I did like the first Sports, and the some of the games on the two Wii Plays), Animal Crossing, etc.