My favorite arcade game growing up was PINBALL!! The good old analog variety at the local bowling alley. My favorite one featured Elton John... the ubercool "Captain Fantastic and the Brown Dirt Cowboy" game. Um, yeah. It was a long time ago. What can I say? ;-)
The first electronic game I played at home was pong. On our gigantic TV. Then we got a really exciting (not) game called Tank. Then there was this clown game I got for my Commodore 64. You had to launch a clown in the air and he would pop balloons on the pointy part of his clown hat... or something like that. Not sure how I could be addicted to this game, but I was.
I did get to play REAL games (like Frogger, Asteroids, Ms Pac Man and Space Invaders) at my friends' house on their cool new "toy" called an Atari. Years later I was addicted to the PC versions of Descent and Solitaire. Odd combination, but it worked for me. These days I enjoy Ricochet (aka Rebound), which is like a futuristic version of pong, really.
My favorite arcade game now is still pinball, although the opportunity to play it is rare. I occasionally play the pc version (I really like the table layout in Win's freebie version), but nothing feels like the good old Bally or Gottlieb originals. :-)
Okay, sadly, I totally remember that clown game. I think that was the start of my clown phobia.