The first games I truly remember playing were the old Freddy Fish games! My grandma also bought us "American McGee's Alice" when I was incredibly young. (LOL,) But I have vivid recollection of playing the heck out of that game.
Considering how fuzzy my childhood memory, I think it's crapshoot between Golden Axe on the SEGA Genesis, Commander Keen on MS-DOS or Doom 2: Hell on Earth. I think the much more obscure Operation: Inner Space is another contender for "First game i've ever played" cuz that's just how bad my memory is.