What is the puropse of the other choirs of angels? There are nine choirs of angels: Seraphim, Cherubim, Thrones, Dominions, Virtues, Powers, Archangels, Principalities, and Angels.  What do the Thrones, Dominions, Virtues, Powers, and Principalities do?  Are they just in heaven praising God, or do they have some special function in the universe?
The choirs tend to be considered part of the extra-Biblical tradition of the Catholic church, with some attributes derived from historical Judaism.  While I'd always recommend Aquinas, if you're just curious in an overview, I'd highly recommend our friends over at Catholic Online:

http://www.catholic.org/saints/angels/angelchoir.php

The nature of the choirs seems, to me, to be a way for the fundamentally limited human mind to understand something of the nature of heaven, perfect, and the presence of God.  You asked specifically about Thrones, Dominions, Virtues, Powers, and Principalities so I'll delve into those a bit:

Thrones are a relay between some of the other orders of angels and God.  They epitomize humility.

Dominions are a relay from God to some of the other orders of angels.  They epitomize regulation.

Together, Thrones and Dominions provide communication to and from God.

Virtues control the elements.

Powers are the professional warrior class.

Principalities are, in my opinion, a complete theological hornet's nest.  They seem to exist to demonstrate the supremacy of Jesus but are pretty difficult to explain in a single line.  You might want to read up on them in greater detail on your own.

Of course, this is just one interpretation, you may also want to check out Wikipedia's (http://en.wikipedia.org/wiki/Christian_angelic_hierarchy) or track down the verses in question yourself.

Or, of course, you can throw up your hands and just read Aquinas.  The Summa is an immensely rewarding read and I highly recommend it.