Dreamcast is number 1 for me. Had Sega supported it through the whole generation I doubt I would have bought all three of the other consoles. My only regret? That Agartha was never released. I would have like to have seen the Castlevania came too. Other than that, a first rate console with great first party games and some fantastic (albeit few and far between) third party games.
PS2 - It had some true classics in there amonst the shovelware. Games like Ico, SoTC, Mark of Kri, Burnout 2, God of War, Prince of Persia and Okami bring this console up to second place. I do sometimes look at my games collection and wonder what the hell I was thinking though. A fault purely with me rather than the console.
Gamecube and Xbox usually tie but the often jostle for 3rd and 4th place - which is not to say I dislike either, just that they didn't offer as much as DC or PS2 for me.
Gamecube - I'll admit, I bought this in the expectation that it was going to get uber levels of support from Sega. I'm rare in that I don't buy Nintendo consoles for Nintendo games and Sega seemed a perfect fit for the console. In the end I bought very little for the Gamecube, but what I did buy were some of my favourite games of the generation. Resi Remake, 0, 4, Super Monley Ball, Eternal Darkness, Rogue Leader and Twilight Princess are all I own.
Xbox was a similar deal, I bought it for the Sega exclusives (specifically JSRF but also the dubbed version of Shenmue 2 and Outrun 2). I probably own a similar number of games as I do for the Gamecube (slightly less) but it was a great console and lead to my favourite console of this generation.
Gamecube. I remember the record level of disappoint towards Wind Waker back in the day so I'm glad to see the love on show in here. Best controller also hands down. The PS controller is still the only reason I've never bought a Playstation.