I've never been a big fan of Half-elves or Half-orcs, though I don't hate them. Dwarves, Elves, Halflings, and Humans are the classic four (and of course the big Tolkien races, though half-elves and half-orcs are too), and don't bother me at all. I agree with others on Gnomes - I could do without them. The "tinker gnome" concept really annoys the crap out of me.
But man, do I hate Dragonborn. Hate hate hate them. "Ooh look, dragon-people!" Bah. Seriously, WotC's dragon fetish is starting to worry me a little. In my games they're not an available race, though I'm considering using their stats for Half-dragons should the need ever arise.
And while I like Tieflings as a concept, I don't like 4e Tieflings (tails?!?); they should have been in the MM (or better yet, only in the FR books, where Planetouched are a much more common concept). What I really want to know is, if there are Tieflings, where are the Aasimar?? I find it odd that an addition which really pushes the "good guys" concept fails to include Aasimar; they balance with Tieflings, and their traditional stats (i.e. the Cha bonus) make them good Paladins, just like those stupid Dragonborn. Confusing, I tell ya.
Mor