I could see the following guys go:
Washburn, Batista, Dickey - Might be overpayed, but contracts aren't overly burdensome. Teams like to pick up vet pitchers to show the fans they're trying. Dickey and Batista can both throw from the pen, so they might have value as swing men.
Bloomquist - could go to some team for a marginal prospect. As injuries mount around the league, his versatility can be useful to a contending team.
Ibanez - hard to see an NL team taking him unless they want to stick him at 1B. I could see an AL team picking him up as a part-time DH/1B/LF.
Rhodes - sure. Lefty setup guy? Popular choice to go.
Sexson - Hard to see it unless his production really picks up. Then someone might take a flyer on him as a 1/2 year rent-a-player. Would have to be a unique situation.
Lopez - Probably already playing at peak performance, so if he goes, he might command the best return. Has been steady this year, but doesn't have a high ceiling.
Bedard - I just don't see it. If healthy and strings together a few quality starts I can see offers come in, but I don't think the team moves him for less than a blockbuster deal.
Vidro - switch-hitting veteran could be cut and picked up, or traded for a marginal prospect.
Putz - I don't see it happening. Seems like at mid-year teams like to take other teams' marginal closers and make them their set-up men. If a team like the Tigers were in contention I could see it because Todd Jones has to make them nervous.
Beltre - Prohibitive contract. Mariners would likely have to sell cheap. I'd say hold on to him if that's the case.