I started out in the arcades, because there were no home consoles, except the Atari 2600 and its copy-cats. My neighbours had one and I used to play spyhunter for hours on end. It was better with the wheel in the arcade though.
I've never owned a console, but the Commodore 64 was pretty close to one, only it had a word processor as well, and you could make your own (crappy and simple) games. My brother got a Mega Drive when they were brand spanking new. I played Alex Kidd on it (of course) and Road Rash and the Buck Rodgers RPG, but for me I always came back to the computer.
Edit: I guess we are called Generation X (What's the name of my DJ?) I was born in 1975 and for my childhood gaming was Monopoly and Mousetrap.