I sent away for these records to the National Archives in Washington, D.C. Getting records from there, depending on what you ask for, can be pricey, but they have a lot of good stuff archived and the records usually get shipped pretty quickly.
I wanted Charles Haase's muster roll records because I had the date he enlisted in the Army, and the date he was discharged, but I was curious as to where he spent his time in between (it was less than a year that he served). I know his unit took part in General Sherman's March to Sea, but as I've learned from my research, unless you're so lucky that you have a muster roll for an actual date of a battle, you really can't say for certain what aspects of the war your ancestor took part in. Of course, a muster roll does give you a general vicinity in which that person was at that time, so if your ancestor was recorded as being in New Jersey in October of 1864 then you can be fairly certain he wasn't part of, say, the siege of Atlanta.
The muster rolls are somewhat informative - if I hadn't known for example that Charles was a hatter by trade, I would have found out from these records. It can also give a description of the individual, his possessions, what he owed, etc.
I have one muster roll for Company H of the 33rd New Jersey Infantry: "Charles Haase appears with rank of private...roll dated Trenton, N.J., Oct. 23, 1864." It says he was born in Germany, is age 35, occupation hatter. Drafted and mustered in Sept. 22, 1864, Newark, N.J. for a period of one year. His eyes are blue, hair is light, complexion is dark, and he stands 5'7".
One one roll he's charged 8 cents for a cartridge box plate and "also 23 cents for screwdriver." On June 1, 1865 he was present in Bladensburg, Maryland, which is when and where he mustered out. He had drawn $72.77 from his clothing account. On July 17, 1865 he was in Washington, D.C. where he still owed money for his clothes. In another, it says he was drafted out of Union township in New Jersey.
Even if these records don't tell you anything new, the fact that they're repeating the same information you already know helps to corroborate the information you have. The more you can back up your research, the more accurate it probably is.
You can find the National Archives at www.archives.gov.