I honestly don't remember! The first game I vaguely remember playing is Mortal Kombat on the SNES, and I think I was 3. Then again, it may have been Mario Bros. on an Apple ][gs (I got the weirdest hand-downs from my cousin). The first game I remember clearly actively playing is Phantasy Star IV. The dark tone of the game really blew my 5-year-old mind.
My dad had a SNES (that he gave to me a while back) that I played Super Mario All-Stars, Donkey Kong Country, and Pitfall - The Mayan Adventure on (all some of my favorites to this day) but the first game I got with my own money was DKC2, and I still think it was one of the best games I've ever purchased. The first system I bought myself was a Gameboy Color with Wario Land 3 (which took me a while to figure out but it was also very fun).
Not the oldest on here obviously, but my parents had a Tandy-1000 (I still regret not having that machine) and I had a few games for it, like treasure mountain, and a few failed attempts at the Hunt for the Red October game my dad had, as I recall there was also a collection of fairly simple ASCII games, like a hand full of card games, a pac man clone using the little face character, and so on... But I think I really started enjoying video games with our second computer, which had Civilization (one), and also TIE fighter when we got it (Second hand, it also had Stunt Driver which had one of those manual based copy protection systems. Guess that means I've been a software pirate for some time too >.> "Before a turn, press down on the ____ to slow down.. Page 25, Paragraph 4, Word 43" Too bad there were another fifty or so questions I didn't know.