I think the best example is Star Wars. The universe was big, and the West End RPG literally expanded the expanded universe to a huge degree (I recall a story about Timothy Zahn receiving tons of Star Wars RPG books when he was going to write the Thrawn Trilogy).
I think other properties wish they could get that kind of setup: a widely known setting that new and old players alike can come into and have a shared perception of what it is.
As for players, the big deal is definitely wish fulfilment. I think a lot of people see/read/experience something and go "Wow, that would be cool, if I could ..." The best properties have a ton of open space wherein you can do that and not be restrained, but there are plenty of properties that can be too tightly focused. I think some great games have come out that were limited by their property (Robotech), while others were great properties that were limited by the system (um....Robotech again? Actually, also the Aliens RPG). Both situations can be overcome, but the key is to not have these issues in the first place, because then the game's accessible (people know the world through whatever media it appeared in), has lots of open space (so people can come up with lots of ideas of what to do as player characters in this setting) and the system doesn't scare them away.
Again, I think those aspects are what made Star Wars a great RPG property. Buffy also worked because you already had several spin offs, which is basically like a big example of "See how we can make this different, but still work in the same coherent place?"