It was a tough choice, but in the end I voted Half-elf. There's just no compelling reason that in a game where humans and elves have been fully playable race options from day 1, Half-elves should be an important core race. They either have no niche of their own, or (as in 4th) end up as a weird unique race that has nothing in common with either of it's parents.
There's plenty of other worthy contenders though.
Half-orcs. Now, don't get me wrong, I played a ridiculous number of Half-Orcs in 3rd edition, and enjoyed most of them, despite the mechanical weakness. Their orgin is...problematic though, to say the least, and there's really no need for them anymore. Back when playing a "monster" race was unthinkable, playing a Half-Orc probably seemed like the next best thing, but few people these days would blink at the idea of playing a full-blooded Orc, which eliminates the need for another boring Half-race and neatly sidesteps the messy orgin issue.
Halflings. They have more traction than gnomes, but they've always teetered on the edge of critical unpopularity, and have been revamped several times as a result, without ever really taking off. Winning a close-fought popularity contest with gnomes isn't exactly a resume winner. They do have their niche though (small, fast/sneaky guy) and are unlikely to ever be fully replaced by another race, so I imagine they'll continue hanging on they like always have, without ever being truly popular.
Gnomes. Eh, it's been said many times elsewhere. I personally always like gnomes, if only because they seemed to get virtually zero support compared to even unpopular races, but I have to conceed they have no real niche, distinct identity, and have always been the forgotten core race. I like some of the 4th edition gnome changes, but I don't know if gnomes can ever really be salvaged as a race, after 30 years of being known mostly as the butt of gamer jokes.