I like weird races, but they need to have justification, and it can't be overdone.
In my ongoing Eberron game, there's usually an easier solution for any monstrous concept, just because racial HD and LA are so detrimental. (I had a player want to play this intelligent golem from the MM5, if I recall, that lacked an LA. I looked it over, and told him, "Seriously, man, just play a warforged, it's almost exactly the same creation concept, AND you have much better mechanical support.")
I had one of my top RPers want to play a half-dragon Kenku. The combo was a bit odd, but he really liked the idea, and eventually we came up with an interesting backstory for the guy. (Kenku in Eberron are described as having a spy-network, so we figured his dragon parent had been a Chamber member who was trying to get in on that information access.)
But in the meanwhile, someone else said "Ooh, cool, a half-dragon? I want to be one too!" I had to put a kibosh on that, because multiple active half-dragons, in Eberron's very strict dragon-controlled setting, does start to strain credibility. (Of course, now, that player has decided to retire the character, so now if someone else wanted to make one, I'd be good with it.)