For all my pickiness about a campaign world (I'm nearly always the DM), I don't have many preferences on this issue. I can pretty much rationalize whatever the players want to do, one way or the other. In fact, the players are more likely to impose some restrictions on races, amongst themselves, than I am. They often want a good mix in the group. So they talk about what people are planning to play, and come up with a mix that makes everyone happy. Fortunately, we all get along well. Thus, we've never had a conflict over it.
When they used to do everything independently, we did get some weird groups. I remember one 3E campaign where one of the players that usually is the "steady" sort decided to build a slightly crazy, dwarven ranger, with some "issues". The abilities selected were a little off beat, too. He was planning to be that guy that "sticks out" for a change. He did stick out. He was by far the most "normal" one in that group--out of 11 characters, including two or three humans.
Mechanically, I've always appreciated the way DragonQuest did this. You had to have the right mindset, but for a game with an odd mix of choices and random char gen, it just worked. You got three tries to roll for a non-human race. Each race had a percentage chance, based on its numbers in the (default) setting. So it might be 30% for a dwarf, but only 6% for a shapechanger. If you missed all three rolls, you played human. So you could go after the exotic options if you wanted, but if you really didn't want to play human, you were better off to go after elf, dwarf, etc.
Note that this worked better in DQ than it would in a D&D 3.* or 4E game, because the mechanical racial advantages in DQ were both most severe in effect, but less absolute in scope. That is, elves got a very nice XP advantages playing characters wih the "courtiers" profession, but this advantage wasn't definitive. It was alright to forgo it, and alright for non-elves to be courtiers.