Ever since I was a kid and read the Animorphs books, I thought it would be cool to play as them. Or even just take part in the Yeerks and Anadalite war.
Glen Cook's Black Company would be cool. Not only are the characters interesting, I find the setting really cool with the fantastic elements but maintaining that most people have little magical aid, even if they know a mage.
I may be dating myself with this, but I was surprised not to see it mentioned (I don't think). So I will mention Harry Potter. That was such a missed opportunity for the industry to maybe interest a new generation of players.
It could have made a great setting too, if you like it. Not perfect, but plenty of possibilities.
Oh, and I'd like to add an odd one: the Civilization series of computer games. Each player could be this immortal ruler of their people, complete with the ability to somehow teleport to meet each other face to face. Their civilizations could be developed too, like with its own character sheet. Maybe a little like Birthright. It's a little unusual, but something I've thought of while playing. The kind of fantastical addition of this immortal leader on top of an otherwise normal history makes me think of it.
For you Wizard of Oz fans there is an Oz game called Oz: Dark and Terrible. IMO I think it's pretty cool.
Now, for properties I wish got the full RPG treatment... in no particular order...
The Elder Scrolls
Legend of Zelda
Xenogears (or is it zenogears? I think it has an x)
Harry Potter... talk about a true missed opportunity.
Wheel of Time ... not the d20 one but an updated one with better mechanics.
And I'll give a passing nod to Power Rangers... not so much because I like it, but for as long as the TV show has been on, all the toys dominating store shelves for over a decade and kinda like Voltron in a way and it's popularity among kids... it could have been a possible introductory game into rpgs for kids... like Harry Potter could have been.
I forgot, the Temeraire series would also be nice.
Fresh scenario (Napoleonic area ... with dragons) and a good way to bring groups together (Crew of a dragon). Only problems would be to find a system which can handle muskets and keeping all players occupied during aerial combat.