Let's eliminate options: here are some positions the Vikings will not fill in round one of the draft this weekend. Though I probably shouldn't say that; I should say if the Vikings do draft a player at these positions in round one, I'll pour two beverages over my head. I'm of course ignoring kicker, punter, returner, long-snapper, etc.--business like that.
The Vikings have Adrian Peterson and Chester Taylor: there's no chance they use a first round pick on one of their biggest strength, especially when their superstar running back is entering his third season. Fullback is a major weakness, though I don't know if there's a fullback they'd draft in round one.
The Vikings aren't going to draft a replacement for either E.J. Henderson or Chad Greenway. I doubt very much the Vikings are trying to replace Ben Leber (he's a quality starter), they're extremely unlikely to try replace him this season with a first-round pick, and it's virtually impossible that they'd draft a linebacker in the first round to improve depth or gain a starter later than 2009. The Vikes lack depth at linebacker, but starting linebacker is another team strength.
And that's all I've got. They have serious needs at offensive line. I think they could use improvement in the secondary (I'd like to see them draft a cornerback). They could always use another wide receiver. They might try to get a young defensive lineman (to eventually replace Pat Williams, or to immediately replace Ray Edwards). Things could get freaky and they could find themselves with a quarterback.