Am I like the only person who posted here that owns all three?
Anyway, my favorite would have to be the PS1. The Genesis does have good games, but I feel that the Playstation has more great games, such as Spyro and Final Fantasy games. The Dreamcast, even though I love it to death, doesn't have that many classic games aside from Sega games, Soul Calibur, and Marvel vs. Capcom.
PS1 for sure. I was going to say Dreamcast, but then I remembered that all of my favorite Dreamcast games were also released on the PS1, except for Power Stone (e.g. Soul Reaver, Jet Set Radio, and Hydro Thunder). Also, the PS1 had FFVII, Tenchu, and the original Silent Hill. How much more awesome can you get?
Nintendo 64 smokes all three of these though.
The PSX, no doubt. What with Metal Gear's fourth wall breaking, and the Legend of Dragoon, I was all set as a kid. Never having gotten a Final Fantasy game, I feel as if I cast away the PSX without ever really owning it.