I'll go with some text based ones...
It would obviously (to those in the know) be silly to mention anything by Infocom, so I'll try not to.
One of my all time favorites is Hound of Shadow, a Lovecraftian text adventure ("Interactive Fiction" if you like elitist sounding genre titles - I'll go with "Text Adventure" any day.

). It had an almost RPG like character creation process, in which you selected skills, which had some (very small, sadly) effect on certain puzzles and situations. It also was quite charming in that you could pass the time strolling about London (I think it was London), checking out things while waiting for the plot to advance.
An old time favorite was Perseus and Andromeda, which was, surprise, based on Greek myths.
Gremlins, the Text Adventure, entertained me a lot on my C64. You can guess what that was about.
Also, if you want to go really classic, Scott Adams' Adventureland, or anything by Scott really. (Well, I wouldn't actually touch any of the Marvel Games, The Hulk, Spiderman, or Fantastic Four, as they were quite poor.)
Let's see, anything else..? All right, just one more, graphical, not text: Superhero League of Hoboken, which is an RPG/adventure hybrid by Legend Entertainment. I'll bring this game up in all threads if I can, I adore it so much!