It was Either Doom, Wolfenstein 3D, or Rise of the Triad, and I would have been 5 at the oldest. These games all came out before the rating system, so my parents were less strict at that point. Once the ESRB was fully entrenched, my parents -- moreso my mom than my dad -- started paying attention to the ratings. I didn't get a new M rated game until I got Shogo at the age of 11 or 12, and I still had to fight to get the M rated ones until I was 15 or so. However, it wasn't as big of a deal when I was growing up, because companies were still putting out large numbers of E rated games that weren't shovelware, as well as plenty of T rated games.
I feel bad for kids with strict parents today -- I can't remember the last time I bought an E rated game that wasn't old, a handheld game, or shovelware. Aside from a few really old games I've picked up cheap, every game I've bought since I got my new computer has been rated M, and it's because that's what most games are rated now, not because I'm some kind of Mortal Kombat loving vampire; I went through that phase somewhere between seventh grade and sophomore year of high school.