Branyan was made expendable because the Diamondbacks needed to make room for Micah Owings on the 40-man roster. He is only one year removed from hitting 19 HRs in 322 PAs against right-handed pitching, so there will be a team out there that could use someone like Branyan.
Teams that might show an interest in Branyan are:
Cleveland Indians: With Travis Hafner out 2-to-3 weeks, the Indians could use a left-handed bat against righties.
New York Mets: The Mets reached .500 last night and they could use another 1B and a power hitter off the bench.
Cincinnati Reds: The Reds' only lefty off the bench is Fred Lewis. Like the Mets, they could use a power left-handed bat off the bench.