I think the first time I ever did this was back during DOA for the extra menu options that helped make the game easier to unlock all the characters and costumes. Then it continued to other generations of consoles.
32 Bit Era
Dead or Alive(PS)--for extra menu options
128 Bit Era
Marvel Vs Capcom 2(Xbox+PS2)--for points in training mode to unlock extra characters
Current Gen
Bullet Witch(360)--for the 15 total hours of playtime achievement.
What about you guys?
EDIT: I changed the title to make it alittle clearer. So it's basically if you have ever left your console on over night for time release stuff, leveling up, refusing to have to start at the beginning of a game(with no save or password features) once you're put serious time into it or anything else you might have left your console running for.