My very first video game experience was with Resident Evil 3. My brother bought it a few days after it had come out in stores, and would play it in the loft and let me watch.
It scared the bejesus out of me, but I'd try and play it when he was in the bathroom, resulting in sobbing and being yelled at for messing everything up.

My first kid-friendly game was probably one of those Rugrats games, or Banjo Kazooie.