In his most recent Ask BA column, Jim Callis gives us a list of comp free agents as well as a few scenarios. There are only 15 Type A free agents, and I'm thinking something like five of them will actually change teams and require forfeiture of a first or second rounder.
The Rangers would be one of those five or so if they manage to sign Torii Hunter or Aaron Rowand. Since they have no compensation free agents after dealing Ron Mahay (Type B) and Eric Gagne (B) at the deadline, Texas will either have their normal allotment of picks next June or, if they do sign one of those two CFs, be only without their second rounder.
No one looks likely to clean up quite to the degree that the Padres, Rangers and Giants did last year, though the Red Sox, Mets and Phillies do have outside shots at that, if they lose all of their players for the maximum and don't have to give up their own. In theory Milwaukee, St Louis and San Diego could have as many as five first rounders (including supplemental round picks) as well, but that seems very unlikely.