Round 1 - 12th pick (12th overall)
Round 2 - 11th pick (43rd overall)
Round 4 - 9th pick
Round 5 - 8th pick
Round 5 - 19th pick (from the New York Giants in the Sage Rosenfels/Darius Reynaud deal)
Round 6 - 7th pick
Round 7 - 13th pick
We can't put an "overall pick" number on anything after the Vikings' first two selections, because the compensatory picks that the NFL gives teams that lose free agents start in the third round, and those haven't been announced yet.
I had thought that the Vikings had more picks than this, but it turns out that the draft pick involved in Jayme Mitchell being dealt to Cleveland and the pick that came with Randy Moss from New England are both 2012 selections. The Vikings got a seventh-rounder from the Patriots in 2012 as part of the Moss trade, and they received an "undisclosed" draft pick from the Browns in exchange for Mitchell.
Mike Wobschall points out on the Vikings' official site that the Vikings have selected 12th overall only one other time in team history, and it turned out pretty well when the Vikings picked some running back named Chuck Foreman out of the University of Miami. Hopefully our pick at #12 this year. . .should the Vikings stay in that spot. . .will turn out just as well.