The Detroit Tigers, of course.
Detroit receives Jose Iglesias, a young shortstop who is a wizard with the glove and has shown some promise with the bat at the Major League level -- a point of much polarizing debate for many fans in Boston. But even if he bats .220 for the rest of the season, he improves the Tigers' team fielding (which, surprisingly, hasn't been that bad this year) by taking over for an average Jhonny Peralta; who is just going to get suspended anyway.
With Iglesias at short, he makes up for some range lost by having Miguel Cabrera play third base. This will improve Detroit's starting pitchers, who were already doing a decent job of pitching around their defense to get outs and wins. Max Scherzer leads the AL with 15 wins, and only one Detroit starter has an ERA above 4.00.
The Red Sox get Jake Peavy, but they have opened up third base to be manned by a revolving door of minor league players. If Stephen Drew suffers another injury, then both shortstop and third base will share that revolving door of minor leaguers. Bringing prospects up has worked well sometimes for the Red Sox this season -- see, errr, Jose Iglesias -- but the Red Sox have placed themselves in a position where they are depending upon undependable wildcards at third base for the rest of the season. This trade has the potential to blow up in Ben's face.
Peavy hasn't been that great this season, either. It could be argued that Brandon Workman would have done a better job starting games. We'll assume, right now, this strengthens the pitching staff by getting an experienced starter and placing a promising prrospect in the bullpen. We're going to have to wait and see, though.
As for Chicago, they get three prospects that nobody really cared about.
To summarize the Peavy/Iglesias trade: Detroit fortified their team, Red Sox may have improved their pitching but left themselves a ticking timebomb at third base. If the Red Sox make it to the ALCS, Detroit will likely be waiting for them. I'd hate to see Iggy playing well in such a situation.