My favorite older console is probably the GameCube, personally. Twilight Princess and Wind Waker come in at a close tie, with Twilight Princess having maybe just a little bit of an edge to it.

I do not have a GameCube anymore, but I did purchase a Wii fairly recently (2~ weeks ago) after not having a Wii nor GameCube for several years, and as a result I've been enjoying City Folk very much (for the first time)! With the purchase of the Wii came some classic GameCube favorites, so I do have Twilight Princess today! (I managed to get a copy of it in near mint condition, not a scratch on it, has the case, booklet, etc, for only $45. Isn't that just incredible?)

SNES with Terranigma as my all time favorite game. They're no longer in my possession sadly and the game is difficult to find as it was never released in North America (I live in USA). There are so many good games for SNES that I could go on forever but Chrono Trigger, Secret of Mana, and Link to the Past are up there as well.

Playstation 2 is my favorite older console and yes I still have it.  I really like Dance Dance Revolution Supernova and The Game of Life (technically for PS1, but it still works on it).  

DDR was my jam! I had it since PS1 days and got the mats + went to arcades. PS2 is my fave second, I've logged many many hours on it thanks to DDR, FFX, and Okami.

I have almost all the Nintendo consoles except for the Gamecube. My husband sold the GC a long time ago since the Wii can play those games, and I really regret it because I am a collector. I hope we can buy it again because I think it's my favorite console along with AC as my favorite game. I also like the SNES and Super Mario Kart (still my favorite version).

Gotta go with Sega Genesis, and I had a lot of favorites on it. Believe it or not, they're not Sonic games, but games like Castle of Illusion Starring Mickey Mouse and (don't laugh) McDonald's Treasure Land Adventure.

And yes, I still have them. We had to replace our old Genesis some years ago, but that's what places like Vintage Stock are for.

Does the Nintendo DS count yet? It did come out in 2004. If so, I pick that. My favorite game for it is Animal Crossing: Wild World.

Super NES - Robotrek. I do still own it, but it doesn't work (which stinks, because being a child, I never beat it). It was a pretty obscure game, but it was pretty fun. And VERY Japanese.

Easily the Wii, which I still have. Zelda: Twilight Princess and The Conduit 1 + 2 were some standout games!

Nintendo 64! My favorite games were Super Mario 64 and Mario Party.

I have many old consoles that I like a lot so it'd be tough to choose (I have an NES, heavily modified Model 2 Sega Genesis, a Model 1 Sega Genesis, a Nintendo 64, a PS1, two fat PS2s, a blue original DS and 4 Wiis) but out of all of them, mine would have to be the Wii since I have the fondest memories with it, Wii Sports Resort is a classic and I loved lots of the games available on it, such as New Super Mario Bros Wii, smash brawl, etc. I still have my first Wii from my childhood but sadly it is very close to giving up the ghost it hasn't been able to read discs for at least 5 years and it crashes constantly

I forgot to add Star Fox 64 and Ocarina of Time. D'oy