On my phone I play a lot of Gameboy/Color RPGs. Zelda, Pokemon, Final Fantasy Adventure, Dragon Quest, etc.
Generally speaking though, I play whatever I feel like playing at the time. I love shmups and beat em ups (obviously), but I really enjoy anything I can play multiplayer. So that means a lot of SNES and Genesis, with the occasional PC-Engine thrown in the mix. If I'm alone, PSP is great too.
Dreamcast, of course, never gets old for me.