The Nine Angelic Choirs ranking system for angels was developed by a theologian in the sixth century. Dionysius the Areopagite's system was endorsed and accepted by the Catholic Church.

The Seraphim

The Seraphim are considered in this system to be the highest ranking angels and sit at the hand of God. They spend most of their time continually chanting "Sanctus Sanctus Sanctus Dominus Deus Sabaoth" (which translates pretty much into "Holy, Holy is the Lord of Hosts, the entire earth is full of His Glory"). They are associated with healing fire, are said to have sixteen faces and a radiance which makes it impossible for any creature, or other angel, to look upon them. They are also usually described as having three pairs of wings.*

The Cherubim

Mentioned in Exodus 25 as having carved the figures (or simply having been the figures depending on the biblical translation) for the Ark of the Covenant. Also said to have been posted at the entrance to Paradise after Adam and Eve were politely asked to leave. They are said to have two pairs of wings and four faces and stand for eternal vigilance and knowledge. Sometimes they are said to drive God's chariot for him, serve as a bookkeeping service, and maintain the hosts of heaven.

The Thrones

"The many eyed ones who serve as the wheels of the chariot of God." Sometimes called the Ophanim. They are said to have been assigned the task of fulfilling the justice of God. Their power lies in humility. Although they are said to shine as brightly as the Seraphim and the Cherubim, their humility allows them to objectively pass judgments on behalf of God.

The Dominations

Administrator types who are said to prefer wearing green and gold outfits and carry both a sword and a scepter. They regulate the work of other angels and keep a close watch on even the most intimately small details of existence.

The Virtues

Also said to perform administrative duties similar to those of the Dominations, but they are most specifically assigned to the details of our world and the cosmos. They are said to keep planets and stars moving in their proper order and looking after the weather on earth. They also are said to do a bit of work with bestowing character, such as valor and truth, in the souls of mortals. They are the patron angels of saints. According to Thomas Aquinas they regulate miracles as well.

The Powers

Sometimes referred to as the Authorities, they are said to have the task of hitting demons over the head if they attempt to take control of the world. They guard the pathways between heaven and earth and assist humans in resisting temptation. It is this class of angels that Lucifer is said to have once been, and the class from which he drew his greatest following during the fall from grace.

The Principalities

Said to look over the goings on in cities, towns, houses and any structure that contains humans. They are said to be given fairly frequent permission to deal one on one with mortals. They work forms of miracles that are overlooked generally and greated as "hey, an odd thing just happened... how strange, I guess everything is going to work out after all." They hold the power to move the hearts and minds of humankind when deemed necessary. They tend to aim for guiding and regulating the ideas of world leaders for maximum results.

The Archangels

The most historically ambigious of the angels, sometimes considered leaders of the entire angel command. This stems from the original angel hierarchy where there were only two types of angels, anchangels and run of the mill angels. In Dionysius' model they serve the Will of God in direct relation to mortals. Their close association with mankind leads to their low ranking in this model. They are field commanders in the battle against evil and the fallen angels under Satan's command. To mankind they impart comfort, solace and inner strength through unconditional love, usually in the darkest moments.

The Angels

They don't get a special name, although sometimes they are called the Guardians or Guardian Angels. They are said to focus on being caretakers for mortal humans. Their position is said to be no lower than that of the Seraphim in the eyes of God and they are content with their position in the choir.

*Special thanks to Dann for the original Greek translation of the Seraphim chant: "Αγιος αγιος αγιος κυριος ο Θεος ο παντοκρατωρ, ο ην και ο ων και ο ερχομενος."

Seems the Latin is a bit skewed as well, but I can't remember if I ever spoke or read Latin. Dann informs me it should be "Sanctus, sanctus, sanctus Dominus, deus omnipotens, qui erat et qui est et qui venturus est." I confess that my English translation was not meant to be exact, i.e. "translates pretty much into" but I've spent a little time searching and the Latin most often used by sources is what I have above. This is the kind of thing I don't think anyone can translate anyway. The native tongue of Angels probably isn't Latin, Greek or English. The confusion seems to mostly be based on the different Seraphim chant in Isaiah 6:3 and Revelations 4:8.

Some information charted out from
The Catholic Encyclopedia
& "Face of an Angel" by Denise Chavez
& My incomplete thesis "Archangels and the Death Experience" dating back to July 7, 1994.