JQAS: a rudimentary examination of ball-strike counts
The paper compares slugging percentages on various ball-strike counts. Rather than just downloading a bunch of Retrosheet data and figuring it out, the authors watched games on TV. Those games took place between March 20, 2008, and April 20, 2008 (which means they must have included spring training games?), and led to the classification of 1260 at-bats (the authors say 1260 games, but that's obviously an error).
Rather than give the results for all possible counts, the authors divided the data in to "pitcher's counts," "batter's counts," and "netural counts". They did this by "communicat[ing] with 24 individuals who have had extensive baseball experience, including coaches, players, umpires, and sports writers." Eventually they settled on 0-0, 1-1, 2-1, and 3-2 being neutral counts, 2-2 being a pitcher's count, and all others being batter's or pitcher's depending on whether there were more strikes or more balls.
Their results for the 1260 at-bats were:
.5109 SLG in 505 neutral-count AB
.3233 SLG in 566 pitcher-count AB
.5753 SLG in 189 hitter-count AB
These numbers add up to exactly 1,260, which suggests that the authors considered only the count in which the AB was resolved. As has been noted many times, this is less useful than counting the results when the plate appearance *passes through* that count, regardless of where the count eventually ended up.
Because of the small sample size, the authors found no significant difference between the neutral count and hitter's count, but did find a difference between neutral and pitcher's count.
I believe there have been many studies that have examined the implications of ball-strike counts in more detail with larger sample sizes. One of mine is on page 4 here (.pdf). Let me know of any others and I'll add more links here.UPDATE: Tom Tippett study here, courtesy Studes in the comments. Also see Tango's second comment for a few more links.