I remember some discussion a year or so ago about whether entering contests was worthwhile from a sales point of view. I can't say anything about the general experience, but I now have a data point.
My novelette, "A Spirit of Vengeance" made the finals in the 2009 EPPIEs competition. This isn't a huge contest; hardly anyone outside of e-publishing has ever heard about it, and even within that area of the business, it gets variable amounts of respect. Note also that my story didn't win -- it only finalled, making it past the first round of judging.
Finalists were announced in early December of 2008, with lists of finalists posted in quite a few places around the net, and published in some newspapers. The winners were announced in early March of 2009.
Looking at my royalty statements, if we take my third quarter sales for 2008 as the baseline, fourth quarter (which includes less than a month of sales post-announcement) was 125% of that, a modest increase. First quarter 2009 sales were 450% of the baseline, and second quarter 2009 sales were just a bit over 200% of the baseline.
It would've been interesting to see whether second quarter would've been significantly higher if I'd won (aside from the fact that it just would've been nice to win :) ) but it's pretty clear that first quarter of '09, at least, showed a very significant increase in sales. The story had been up for sale on my publisher's web site for over a year by that point, and it'd been up on third-party distributor sites for almost as long; the initial flurry of sales for each of those venues is clear in my records, and both had died down before third quarter of '08.
In my case at least, being an EPPIE finalist did seem to impact my sales, and very nicely too. I have no idea what anyone else experiences, but there seems to be a clear cause-and-effect in my case between making the EPPIE finals and a spike in my sales.