Closers are like kickers in the NFL. Yes, there is the occasional Morten Andersen, the guy who is really good for a long time. Rivera is that guy.
But if baseball history holds in the cases of Parnell and Perkins, then by 2015 the odds are they'll either have lost their jobs or gotten hurt.
The point isn't that a closer isn't important; of course he is. The point is that a lot of guys can do that job -- and that the job is extremely volatile. As Buster suggests, the idea of a Proven Closer doesn't really exist, so when you hear things like "The Tigers need a closer" it's really a bunch of nonsense. What people will really mean is "The Tigers need Mariano Rivera." Unfortunately, he's taken.
Look at the major league save leaders from 2011: Jose Valverde, Kimbrel, John Axford, J.J. Putz, Rivera, Heath Bell, Drew Storen, Joel Hanrahan, Francisco Cordero, Brandon League, Juan Carlos Oviedo, Perez, Brian Wilson, Carlos Marmol, Jordan Walden, Neftali Feliz, Ryan Madson, Jonathan Papelbon, Sergio Santos.
That's 19 closers who all saved at least 30 games. Only four are still doing the job -- the three guys Buster mentioned, plus Papelbon, who switched teams (or five if you count Bell in Arizona, although his hold on the role is tenuous). Joe Nathan missed part of 2011 with an injury, so count him as well if you want, although he too has changed teams. By the way, most of those 19 guys were pretty good in 2011; 14 had an ERA under 3.00.
If you accept that any closer is a short-term job you then start to realize that you just go with the hot reliever on your staff -- in the Tigers' case, Joaquin Benoit should be fine. Drew Smyly would have been fine.
What's more important than worrying about acquiring a Proven Closer is acquiring bullpen depth. So the Twins and Mets shouldn't hang on to Perkins and Parnell simply because they worried about trading their closer. They'll find another one easily enough.