There seems to be an incredibly common misconception, even among great religious scholars, that angels are somehow perfect beings. However, only God is perfect. Angels may come close, and are perfected in the Presence of God, but are not perfect in and of themselves.
Angelic sins are not entirely like human sins, but there are similarities. Angels can be wrathful; extremely wrathful. Generally they won't act without God's blessing, and they almost never act against the Will of God (the consequences are dire, and we'll get to that later.) Angels can be impatient and unforgiving.(1) Angels can be lustful. (2) Angels can be jealous. The biggest temptation for an angel, however, is ego; just look at the fall of Lucifer.
However, there are sins which angels cannot commit. It is nearly impossible, perhaps entirely impossible, for a Holy Angel (not a fallen angel) to lie. In fact, even fallen angels often have to use trickery instead of outright lies, and cannot lie about their name. It is just entirely against angelic form and function to lie, as it is so opposed to God. Any angel can mislead someone, but outright lying is nearly impossible. Likewise, it is a dire thing for an angel to kill any living thing except by the direct Will and Power of God.
The Presence of God is the purifier of all. No soul or angel can be imperfect in the Direct Presence of God. The closer an angel gets to God, the more it is perfected. If an angel sins too gravely, coming into the Presence of God physically hurts, but it is a cathartic pain; they are released from the burden which "sin" puts on their being.
See, angels don't exactly "sin" for the most part. Their misdeeds are not weighed like human misdeeds, and instead have a more direct effect on them. They can be tempted, but falling into temptation causes them discomfort and weakness; nonetheless, it happens. Humans are actually affected similarly, but the consequences aren't as apparent in physical form and are measured differently; perhaps the topic of a different blog post. I digress. When an angel is drawn into the Presence of God, it is purified, strengthened, and renewed.
Certain angels are always in the Direct Presence of God. Among them are Michael, Gabriel, and Raphael, but there are others as well. (3) While these angels do act on the Earth, they are never out of the Presence of the Divine. It would be complicated to explain the ethereal physics of the arrangement, but simply put; God is always close by when they are around. It is in their nature to always be with God, and to always act according to the Divine Will. Because of their link to the Divine Presence, they are also the most powerful among the angels.
If angels were perfect beings at all times, the two most famous angelic blunders of the Bible would be impossible to happen. The first, of course, being the fall of Lucifer, who took a full third of the host of Heaven with him. Get that, 1/3+1 angels rebelled against God! It was the ultimate act of defiance, and it merited them the ultimate punishment which can be meted out upon an angel; to be eternally removed from the Presence of God, and eternally tormented. The fires of Hell are almost a mercy compared to the pain of being removed from the Presence of God and being weighed down with ultimate sin! No wonder demons are so awful to humans, the ones God loves so much. The second is an obscure reference in the Book of Genesis, at the beginning of chapter 6, which is expounded upon by religious philosophers and in the Book of Enoch. This is the case where "Sons of God," in Hebrew, "Bene Elohim," literally, "sons of the gods/God" which most scholars and the Book of Enoch interpret as being angels, saw the "daughters of men" (human women) and made children with them. These angels, though their crime wasn't to the equivalent of the original fallen angels, were punished extremely harshly; however, the punishment described in the Book of Enoch isn't entirely accurate, because it wasn't intended to be.
These are the only stories we have in reliable texts. Some obscure texts, such as the Gospel of Judas, refer to other stories of angels which fell away from God, but their versions of the story are either not accurate enough or too obscure in details for most students to glean much from them. Therefore, I'm not going to reference any one of those texts specifically, rather, I'll tell you an old story which many obscure texts touch on just a little bit, a story about certain angels who came really close to falling.
When the Earth was created, and long before humans existed, certain angels were sent to the Earth to watch over and guide creation. Some of them even dwelt within nature, being like spirits of mountains, volcanoes, forests, deserts, waters, and clouds and storms. It was a great and honorable task, but because they were not Angels of the Presence, and because they were integrated into creation, it meant being almost the farthest an angel can be from the Direct Presence of God, at the outskirts of God's Being.
At first, it wasn't too bad; there were temptations, but most temptations were easily scoffed at and didn't lead to any misdeeds. However, when the result of the War in Heaven was that Lucifer and the other fallen angels were cast to Earth, the fallen ones began to tempt them gravely. They were tempted to all kinds of destruction, and belief in their own power as forces of Nature.
Temptation of these angels grew as intelligent beings were formed on the Earth, as God allowed primitive sentient beings of every creation on the Earth to think of these angels as Divine; it was a primitive understanding and relationship with God, a starting place. Unfortunately, the fallen ones were able to twist the minds of some of those angels into believing that they were actually gods; maybe, not equal to God, but certainly gods in their own rights! They were, after all, among the most powerful forces on the planets.
Some of these angels were also born into human bodies to human women by human fathers, according to the Will of God. They usually did not know of their angelic nature, though most suspected it, and they would live many lifetimes as human beings. They were given an innate wisdom which most people misunderstood, and were always fascinated with things of the spirit world and the Divine. Thus, they could learn, like humans but with an innate insight which surpasses human understanding, and they could teach and guide. Being angelic souls, they have an immense capacity for love, and a strong sense of justice. Most of them are warriors of one kind or another, as well as scholars and priests.
The angels who became full of their own ego and likened themselves as gods met various fates. Some were numbered among the fallen angels, and will suffer that most sad fate of Lucifer and his army. Others were recalled to Heaven, where they underwent a most painful and wonderful cleansing. Still others fell in between, they had sinned gravely enough to not be able to stand the Direct Presence of God, but not enough to warrant being cast aside; therefore, they were allowed to incarnate among the others who already were doing so. They renew their souls slowly through their unwavering service to God. A few, and only a few, were allowed to remain at their posts, and an Archangel was appointed to bring them nourishment from God to keep them strong.
Unfortunately for those who are born among humans, they feel most out of place. They somehow know they're not like other humans, but they don't know what they are. They make up all kinds of stories about their origins, and play on the mythologies of many cultures to explain themselves. They need nourishment from the Presence of God, but they can only find some through spiritual practice, shamanic practice, temples, and religious adherence.
The greatest bonanza for these incarnated angels was the Eucharist. See, Yeshua, the one called Christ, came as the Son of God to renew humanity and to save it from damnation. He brought love for all humans, and the angels who were born among humans did not get left out. When Yeshua instituted the Eucharist, it was primarily for humans, but it was also for these angels. The Eucharist, unlike any other ritual, contains the Divine Presence, and humans take God into themselves when it is consumed. Therefore, the more these angels consume the Eucharist, especially those who have damage from sin to undo, the more they feel the Presence of God; thus, the more they are healed, renewed, and strengthened.
The irony is that the most powerful form of the Eucharist can be found in the Catholic and Eastern churches, even though these angels would be branded heretics by either or both churches if they ever knew enough of themselves to reveal their nature. Of course, most or all other sources of the Eucharist also come from human churches which would misunderstand these beings, and either worship or revile them; either way leading to the doom of those people. In addition to consuming the Eucharist, preferably under both species (bread and wine) such beings also find healing and strength through Eucharistic adoration, reading the scriptures, and other religious activity. Of course, some inevitably are born in Hindu, Islamic, or other cultures and must find the Divine Presence through those paths, but they are more difficult paths for such beings as they do not contain the gift of the Eucharist.
If you think you are one of these angelic beings, incarnated, the best advice I can give you is: live life full of love, forgiveness, and compassion; serve God in every way you can and strive to never harm anyone; participate in the Eucharist as often as possible, but only if you have the right according to the rules of that church; and don't tell anyone what you are, or what you think you are, unless you are absolutely sure they will both understand and not feed your ego because of it. The greatest danger to an angelic being is ego. Human, angel, or otherwise, we are all servants of God, and it is through that service from which comes all power, strength, renewal, and hope.
How much of the above story is true, and how much is allegory or parable to teach a lesson? I would say that at least most of it is true, but it is up to those granted the Wisdom of God (4) to discern.
*** Note on Wisdom texts such as the Book of Enoch, referenced here. These books are not intended to be taken literally, just like much of the Bible itself. They contain secrets which those with Wisdom from God can glean about the nature of angels, humans, God, life, and Heaven. Many of them also contain magic, but the magic is a result of the practice, not really a goal of the practice. That is, you don't gain the magic by seeking the magic, you gain it by earnestly seeking the Wisdom and Knowledge hidden within.
(1) Exodus 23:20-21
(2) Genesis 6:1-2, Enoch 4:1-4
(3) Enoch 20
(4) James 1:5-8
*Vague references in this document allude to stories found in the Koran, the Gospel of Judas, and other texts, but not to an extent warranting citation.