Along with Ryan Howard from the NL, Derek Jeter won the 2006 Hank Aaron Award.

There were two phases of fan balloting at toward the end of the regular season. In the first phase, fans voted on a ballot that included one representative from each of the 30 clubs, as chosen by Major League Baseball. The fans' vote decided which six players in each league would move on to the final vote. Fans then were asked to choose one player per league from those six.
Jeter received 37 percent (29,275 votes) of the AL votes on a ballot that included Ortiz, Vladimir Guerrero of the Angels, Travis Hafner of the Indians, Paul Konerko of the White Sox and Justin Morneau of the Twins.
(Said by Aaron to Jeter) "Seriously, I think this award means much more than just presenting an award to two great players. I think that you, more than anybody, have realized that what you do on the field means little of nothing to what you do off the field. And you have carried yourself that way."

The award is supposed to recognize the best offensive performer from each league so the MVP might soon follow this trophy onto Jeter's mantle and I would strongly suggest reading the linked article, especially the exchange between Hank Aaron and Derek Jeter.