I am a big fan of Dungeon World. It allows the players to customize the class and race through the choices they make. One choice I allow is for the players to choose whatever version they like of their race.
What to be a Tolkienesque Hobbit, Elf or Dwarf? Great go ahead. Do you want to play your halfling like a kender from that other game? Good, you can do that too. Do you want your dwarves to be surface dwelling nomads? Great got room for that. You want to play your elf like a Sidhe or Alfar? Yup head on.
If the players want to play plain vanilla fantasy elf, dwarf, halfling, human well okay no problem. If the players want to go deeper on their character's race, class, history I am more than willing to incorporate that into play.
So what do you other Dungeon World DM's do? Do you have your own settings and stick with that? Do you go with an established canon for a book or supplement? How about guys who play D&D or other more 'settled' games, do you allow player agency in how they portray their race etc? I realize some settings have less flexibility so some DMs and players have less leeway.