Angels, of course, have been around long before Supernatural and are mentioned in Judaism, Christianity, and Islam. They are servants of God who act as a link between Heaven and Earth, and more specifically there are various functions they are said to serve - from smiting the crap out of sinners to carrying prayers to God. Angels are often divided into different groups or hierarchies, the most common of which has nine orders with the highest closest to God and the lowest closest to man. Supernatural, of course, follows some of the more violent job descriptions and they're not so much the "angel on your shoulder" type.
Angels are said to never die, having been referred to as "incorruptible substances" (Guiley, p. 15). Although they have no form, they can appear in human guise or as brilliant beings of fire, light, or lightning. This was seen when Anna regained her grace and promptly exploded in a blinding flash. This does differ, however, from how most angels in Supernatural are unable to take human form without finding a willing host.
As for fallen angels such as Anna, they are often thought - like Lucifer - to fall because of pride, but there are also some who believe they can fall because of lust. Angels are supposed to be sexless (in the biological sense) so sex (in the biblical sense) is a ticket straight out of Heaven. Once they fall, it's commonly thought that they become demons, but it's also been said that they simply become corporeal - in other words, a fallen angel could become a human.John Milton's epic poem Paradise Lost (1667) told a different, more humane story of angels - and the writers of Supernatural have admitted that it influenced their depiction of Lucifer. Milton wrote about fallen angels in a sympathetic manner, so it's highly unlikely to be a coincidence that Anna's last name is the same as his. Milton was also one of the few who wrote about angels enjoying more "human" pastimes - including food and sex - making his name that much more appropriate for an angel who fell to Earth for chocolate cake and love.
So what about Anna?
According to the angelic hierarchy proposed in the 5th or 6th century, Anael falls under the seventh order of angels, the “principalities.” The job of these angels is to "watch over the actions of the Earth's nations and cities - the visible world of humankind" (Guiley, p. 38), which ties into Anna's statement of how she had been stationed on Earth for two thousand years. Anael is also considered one of the chiefs of the principalities, which again makes sense when you think about how Anna used to be Castiel and Uriel's superior.The last piece of evidence to support the "Anna = Anael" theory is the fact that Castiel always calls her Anna. Sure, he knew she had been reborn on Earth as Anna Milton, but she also called him "Cass" without any prompting from the Winchesters. In other words, if you take it that Anna is comfortable using a nickname for Castiel (and has possibly been doing it for some time), why wouldn't it work the other way around?
Random facts: Anael is the chief angel of Friday and governs over the planet Venus. (Ok, so that had nothing to do with anything, but we all learned something, right?)
So now let's all sit back and wait for season five to prove me wrong!