Personally, my favorite race to play is the gnome (specifically the deep or forest gnome). I imagine them as enthusiastically obsessive on certain topics. I'm currently playing a variant human for the extra feat, but if that character dies I've got a forest gnome conjurer ready.
As for more exotic races, they aren't that weird to me because 1) lots of strange, intelligent crearures exist in D&D settings, so at least some of these have to have been accepted by society at large, and 2) one of the first video game RPGs I ever played, Breath of Fire, includes ox, wolf, dog, frog, mole, monkey, armadillo, cat, fish, etc people as members of the party (the fish people are essentially the primary trade merchants of this world, BTW, making trade sea vessels largely unnecessary).
I think playing a minotaur might be fun. 4E's lore for minotaurs sold civilized members of the species to be very lawful and concerned with rejecting the influence of the demon lord Baphomet to the point that they as an extension have also rejected nature, fearing that being in touch with nature could pull out their more animalistic side and make them vulnerable to Baphomet's influence (so minotaur barbarians and druids would be pariahs). Mazes were depicted as a symbolic means of meditation and self-reflection on what it means to be a minotaur and how one must avoid traveling down the paths that lead to savagery.