The new qualifying offer system is much simpler than its predecessors, but it was used nearly as sparingly in year one of the MLB free agency season's new system. The St. Louis Cardinals were one of just seven teams to make a qualifying offer of one year and $13.3 million to an impending free agent—to Kyle Lohse, in their case—and the players involved suggest teams are playing this new rule very conservatively, at least for now. (... Except for the New York Yankees, who used it three times.)
The complete list, via MLBTR, starting with the mess of offers in the AL East: The Yankees used it on Nick Swisher, who won't accept, and Rafael Soriano and Hiroki Kuroda, who just might; the Boston Red Sox offered the deal to David Ortiz, and later roughly doubled it for his new contract; and the Tampa Bay Rays announced their intent to collect the draft pick for B.J. Upton.
Outside that division, the Atlanta Braves offered it to Michael Bourn; the Texas Rangers to Josh Hamilton; and the Washington Nationals to Adam LaRoche. Of those three, LaRoche is the only one who could possibly take the deal; everybody else will be costing their new team a first-round draft pick in free agency.
Thus ends, at least for now, the qualifying offer saga of 2012. I look forward to trying to remember what it means again next year, when we'll have a higher number for that one-year deal.