Bobby Abreu (unless he's changed his tune) blamed the Home Run Derby for screwing up his swing. Anecdotally, there are a few other guys who complained about the Derby. I would imagine that professional hitters, even if they do get themselves out of whack, would figure out the problem within a week or two. Still, let's look at the evidence.
Abreu was never a big home-run hitter (though he had a few big-time years). It's plausible that his line-drive oriented swing (as opposed to an upper-cutter like Ken Griffey Jr.) might get wonky. But, maybe Abreu just got old or regressed to the mean, and it's merely a coincidence that it happened shortly after the 2005 Derby. He hit 18 home runs that year before the break and only six after. He hasn't topped 20 since. Hmm, have we seen the same downturn from anyone else?
Well, 2006 winner Ryan Howard smashed something like 89 home runs after that year's break (or, about 30), so no help there. Last year, Vlad hit almost identical numbers before and after the break. In 2004, Miguel Tejada hit 19 after and only 15 before. You must go all the way back to 2003 to find a drop-off similar to Abreu's: Garrett Anderson hit only seven in the second half after launching 22 in the first.
I stopped looking around 1999, but I didn't see anyone else with an unusually large drop in performance. So, basically, the Derby curse looks unfounded. Maybe the guys that lost the Derby are the ones that truly messed up their swings, but I doubt (if I looked) that would be the case.
So, does this mean I think you should sell Josh Hamilton? I do, but not because of the Derby. He abused his body for a long time, may not be ready to go a full season, and his numbers are so insane they're likely unsustainable. If you can get a Jose Reyes or Hanley Ramirez (any news on his shoulder?) for Hamilton and a middling SS, do it.