Either Missle Command or Asteroids for the Atari 2600 (I believe).
It was at my best friend Mia's house when we were about 7. She only had one because she had a bunch of older brothers. I'm guessing the year (based on my age guestimate) was around 1985. I could be off a year in either direction.
The first console game that really hooked me was Super Mario Brothers for the NES. I imagine I was around 8 at that point...but I don't really remember when that was out.
The first computer game that really hooked me was X-Wing by LucasArts. That was somewhere around 1993 on my family's brand new 486-SX.
Since then, games haven't had quite the hold on me that they used to mainly because I just didn't have the time. There have been a few that I have definitely been a number since then that I have definitely enjoyed and finished.