1st round, 20th overall (own)
2nd round, 52nd overall (own)
3rd round, 82rd overall (own)
4th round, 115th overall (own)
5th round, 145th overall (from Miami)
6th round, 190th overall (own)
7th round, 211th overall (from Minnesota)
My understanding is the Titans currently hold all of their own original picks in the 2012 draft, and no others. The one potential draft pick trade came when the Titans sent the Packers a conditional pick for Quinn Johnson. The Titans cut Johnson when Ahmard Hall's four game suspension ended, though, and the condition failed.
When there are updates to the Titans' draft selections, I will update this post.
UPDATE-Mar. 26, 2012: Compensatory picks have been announced. As expected, the Titans did not receive any compensatory picks. As a result of the Saints forfeiting their second round pick as a result of the bounties, the Titans' draft slot in the third and subsequent rounds improved by one. With comp picks known, slot listings in the fourth through seventh rounds have been updated and are now known good.
UPDATE-Apr. 28, 2012: The Titans traded the 155th pick and the 227th picks (both originally their own) to the Miami Dolphins for the 145th pick.
UPDATE-Apr. 28, 2012 #2: The Titans traded their sixth-round pick from the 2013 draft to the Minnesota Vikings for the 211th pick this year.