According to Storyteller's page, the Blazers have about $49 million in salary committed for the summer of 2012. With Roy taking retirement, his $16.5 million comes off the books at the end of the season. Gerald Wallace has a player option for $9.5 million. If he decides to use it, the Blazers could amnesty him to wipe that salary off as well. This means the Blazers could have as little as $23 million (plus about 6 million for Batum's qualifying offer, Elliot Williams, Babbitt, and Nolan Smith, and our overseas player cap holds). Of course to have this much money you'd have to decline to make Oden a qualifying offer, and trade a few of the younger players away.
They'd have a lot of money to throw at free agents. With Aldridge, Matthews, and Batum, the Blazers still have a good young core. Unfortunately Chris Paul and Dwight Howard would be off the market, Chicago's extending Rose, and the free agent class of 2012 isn't that great (except for RFAs), so the Blazers would have to make a run at Deron Williams, Russell Westbrook, Brook Lopez, Kevin Love, JaVale McGee, Jason Thompson, or Andrew Bynum. If we felt Oden would give us anything at all, then we only need to land one of the point guards, or re-sign Felton.
If we went over the cap to sign a couple of free agents, we could fill out the roster with the mid-level exception, veteran's minimum, and bring over Freeland or Claver on a rookie scale contract.
If we resign Felton, and Wallace leaves on his player option, you could still use the amnesty on Felton if it turns out to be a mistake. Or use it on Oden if he gets hurt again.
The Blazers have lots more options by saving the amnesty instead of using it on Roy, especially since his salary will come off the books anyway.
The amnesty would not be available for use on new contracts (thanks to with_a_z and Sir.Ludo for pointing this out). The best use therefore remains killing Wallace's contract if he opts in. The second best option would be to wipe out the remaining $5 million on Babbitt's contract.
One other thing I forgot to mention: by being under the cap next season, the Blazers can also bid on anyone released through amnesty.