I can't really say I have a favourite. I've had lots of them at one time or another, but usually because of specific games. For example, I had a Gamecube primarily to play the Lost Kingdoms RPG's, a PS1 for the Final Fantasy RPG's, a PS2 for the Final Fantasy, Shadow Hearts and Shin Megami Tensei games... I even had a Dreamcast purely because of one game: The Nomad Soul (how I wish they'd make a sequel to that).
I guess the one I had the biggest library for was the PS2, purely because of the staggering number of RPG's available to it, but some of my fondest memories are of the original Playstation, and playing through games like Parasite Eve 2, Vagrant Story and Final Fantasy VII for the first time.