When Eric Steinbach left for the Cleveland Browns after the 2006 season, the Bengals received a third-round compensatory draft pick -- it was the highest compensatory pick since Takeo Spikes left (which the Bengals used for drafting Landon Johnson). As a result of Steinbach's departure, the Bengals used the 34th pick in the third round for Andre Caldwell. Matt Sherry, Angelo Craig and Mario Urrutia were drafted because the Bengals received a sixth-round and two seventh round compensatory picks for other free agency departures.
How does determining a compensatory pick work? Teams are only awarded compensatory picks when they lose more qualifying free agents than they gained -- if that number is equal, then you're only awarded a seventh round pick after the compensatory picks, provided there's a difference in cost between the outgoing free agents and the incoming free agents. The higher the contract that the departing player signed, the better the compensatory pick will be. Justin Smith could give us a third round pick, and Madieu Williams could be a fourth (if not another third). So you have to go the 2007-2008 off-season, chart the players that left and the players that were signed which will give you an idea of what we could acquire.
Antwan Odom was the biggest free agent acquisition, Ben Utecht was second; Brandon Johnson and Daryl Blackstock were others. Along with Smith and Williams, the Bengals lost Landon Johnson and Bryan Robinson (not sure if either would give us anything). The league typically announces compensatory picks, using whatever formula they use, during annual NFL meetings towards the end of March.