The first I don't encourage, but some players just have a head for maths. The second can work if it's in character, but won't help your likeability. The third, well, is the third truly selfish? Let's talk about that.
There are some archetypes that can be over-powered, or that at least seem more powered than other characters, elves among them, ninja are another, but that's fine, many games allow them. But if you've gamed for any length of time, you'll know a player who really really really wanted to play a race the game wasn't meant to be used by players. That player who really wants to be a Naid, or a Pixie, or a Centaur, or a Dragon. Races normally found only in the Monster Manual. (And of course, there are plenty of sourcebooks out there that eventually made such things possible.)
In my experience, there are really two types of player who ask for these things. One is the gamer who's easily bored unless there's an element of trolling to the proceedings. He wants to adopt strange mannerisms that will bug the other players, or throw his weird abilities in their faces. And it's entirely probable he was just trolling the GM in even asking for such a character, never expecting his request to be taken seriously, and gleeful when it was. The other type of player is the complete novice who's been dragged to a game, and by having no expectations, has every expectation. When I was a teenager, this was the purview of a gaming buddy's girlfriend, or perhaps of my very young siblings when the family decided they wanted a demonstration of this new-fangled hobby I was into. Often, you HAD to let them play this crazy thing or else they would play and whine about it. And it made sense to allow them to have it, because it was probably their only touchstone with that type of fantasy. If the books they loved had heroic winged fairies, why couldn't they play that archetype? They never lasted very long anyway.
So do you acquiesce to these kinds of demands? Depends. If you're an "anything goes as long as they're having fun" kind of GameMaster, you might as well. The biggest hassle - and this depends on the game - is converting a creature into a PC with levels etc., or creating it out of whole cloth, and not have it be unbalanced compared to the players who respect the rules. That brings up another point: The whole group has to be in on the decision; you're not playing favorites. So if you're not as solid as you want to be on the rules, that's a reason not to. If you do anyway, let the player know you might tweak the race/class as you go, especially early on, to be fair and to prevent the game from getting "broken". Another tack is to only agree to a short engagement for the character. After a few games, and perhaps once its "relative level" is passed by the other PCs, its story will end one way or another. That makes sense, because the the character is mostly meant as a novelty. Once it wears off, the player may well be happy to get rid of it and try something new.
Ultimately, there's a lot of joy to be derived from Space Elves, or whatever crazy character your players want to play. Certainly, they'll liven up games and make them memorable. But like anything, they must be used in moderation, and with everyone's consent. And Space Elf players, please, leave the sun alone.