Hmm....That's a hard one.
Arcade-wise it would have to be Galaga or Missile Command, but I did play a lot of Dance Dance Revolution as a kid till all the arcade places shutdown. I know own a Galaga machine I would like to eventually get a Arcade Machine with Missile Command but with current size restrictions in my living space I fear I won't be getting one anytime soon so alas I play down at a local Paracade (Pub that has Video Games)
Playstation: Spyro
Playstation 2: Champions of Norrath Realms of Everquest
Xbox: Tie between Cell Games and Fusion Frenzy and DOA 1, 2 and 3
PC Circa Early 2000s: Warcraft III or Star Wars Jedi Academy, used to play a mod call Movie Battles II, was amazing I still think it's running to this day.
PC 95-2000s: Diablo or Age of Empires II
PC Mid 2000-2010s: World In Conflict, Runescape, and World of Warcraft
Dreamcast: Soul Calibur
N64: 007 Golden Eye
Oh I used to be a giant Pokemon Nerd with the Gameboy->Nintendo DS
but I my guilty pleasure was always Harvest Moon, I couldn't stop playing. Farmville in comparison was a joke.
Franchises spanning multiple systems:
Hitman
Assassin's Creed
Fallout
Quake
XCOM
Favorite RPG to Date: Star Wars Knights of The Old Republic