I've played for a little over 20 years, don't know the exact tally. Maybe towards 23 years.
The first game I remember finishing, might have been Wolfenstein 3D. "Finishing" games in the early-era of gaming was pretty rare, be it the Atari era with games that had no real endings in most cases, or the Nintendo days of brutal difficulty coupled with "One-Chance" to win, as you basically had to get through any game in one shot or reset. So yea, I played a ton of freaking games, but never really finished them.
The last game I remember finishing.. hrmm. Hard to say. Most of the games I get into lately have been really, really long games. So I just keep them on the back-burner and come back to them. So it's either Metro 2033, Mafia 2 or Amnesia: The Dark Descent. Those are 3 games I know that I totally finished.