Tough question! For me, it changes so frequently... like every couple of months! Right now, though, I think my favorite non-Zelda game might be the 2D versions of Cave Story. The game has an excellent plot, great characters, catchy tunes, fantastic combination of modern and retro graphics, etc. This game excels in so many ways and is truly one-of-a-kind!
Mario, Final Fantasy, Kirby, Star Ocean, Call of Duty, Resident Evil, Unreal Tournament despite not having played much, Rise of Nations, Soul, Smash Bros...the list goes on.
My favorites include these franchises: Metroid, Pac-Man, Ms. Pac-Man, Donkey Kong Country, Pokemon, Final Fantasy (the older ones anyway), Super Mario Bros., and the Chrono series. (Chrono Trigger and Chrono Cross)