With the third overall pick in the 2012 NFL draft, the Minnesota Vikings have the first selection that has not already been fully determined. The Indianapolis Colts have now publicly stated that they will be selecting quarterback Andrew Luck with the first overall selection, and there is no doubt that the Washington Redskins will be selecting quarterback Robert Griffin III with the second selection.
Therefore, if any team is looking to move up and guarantee that they get who they want, then the Vikings are the team to call. Vikings GM Rick Spielman has stated that he has been getting phone calls from teams looking to move up and he appears very open to a trade.
With the Vikings in full rebuilding mode, adding as many draft picks as possible would be a great way to help that process.
Spielman has stated that the Vikings rate OT Matt Kalil, WR Justin Blackmon and CB Morris Claiborne evenly and would be more than happy to add any of them to the team. Assuming this is true—though it's likely just a somewhat laughable smokescreen—then it would make sense for the Vikings to drop back a few picks, get one of these three players, and also add another pick or two later in the draft.
In the following slideshow, I'll go through the rest of the teams in the top 10 of the draft and the likelihood of them trading up for the Vikings' pick along with what it would likely cost.