It was probably Mario or Cobra Triangle on the NES but the first PC game was probably Battle Tech.
The set up of the game was so much better than anything else that came out of the mechwarrior franchise though Mechwarrior 2: Mercenaries was a close contender.
But I owned a Commodore 64 and there was some kick arse games on that SpyHunter (I was so stoked when I figured out how to play the bass for that) + Boulder Dash - I killed at that game, I can still remember the sound effects if I think about it hard enough.
Plus through friends I was quite well acquainted with the Atari 2600 (Barn Stormer, Dig Dug, Keystone Capers, Pit Fall), Master System, Mega Drive etc.
My Dad even had those pre-console gaming watch things. Donkey Kong and some diver game, plus he had this cool console (paddle controlled) which basically had Pong and some other cool tank game where you went around a maze and tried to kill each other.
Jurassic Park on Sega Mega Drive was one of the coolest games ever and my friend and I finished it with both Alan Grant and the Raptor.
I think Train Escape From Normandy on the C64 was the first game I ever felt truly proud about conquering.