There are too many oldies I replay time and again to mention here, but I would like to point out three of them: Sunset Riders, Elevator Action and my recent obsession Black Tiger, because all of them are arcade games that I play through MAME without having to locate an arcade carrying them and with no limited credits (and no, I don't feel guilty at all, I doubt Capcom, Konami or Taito would mind that).
Thanks to that, I am now able to finish Black Tiger with one life on the hardest difficulty setting, a feat I could only dream about back in the day.
Some other games that deserve mention for being awesome: Super C (NES version), Code Name Viper, Sanitarium, Revenge of Shinobi, Blood Omen, Silent Hill... The list just goes on.
Guess I'm getting old...