I'm a Christian and I've seen and been constantly exposed to our common view of angels. That said I like Matisyahu who draws from a different culture based in Judaism rather than Christianity. In his music video Sunshine a little girl is featured as something spiritual perhaps an angel. Is this what you all think angels look like? Do you have any drawings or paintings?
Angels are spiritual, not physical, so they don't have a physical appearance. They can, however appear physically in a sort of "disguise", like when the 3 angels came to Abraham disguised as men.
I have never seen one :) But our Rabbis have told us of at least one characteristic of Angels is that they appear to have one straight foot.
The relevance to our daily lives is that when praying the Amidah prayer we are instructed to stand with our legs together in order to resemble Angels.
The appearance of angels is based on Ezekiel's vision in the Book of Yechezkel - Chapter 1
Rabbeinu Nissim, when discussing the law surrounding the depiction of angels, describes them as appearing in visions of prophecy as אדם שיש לו כנפים, a person who has wings.
I have found other descriptions of angels in the Talmud. Before I mention them, I want to stress that while the Sages' words seem to describe some angels in a certain way, one mustn't discount the deeper, metaphorical meaning of these descriptions, which certainly yields the most truth and wisdom. The suggestion of visual representation is merely a means to an end; an afterthought, if it is true at all.
The Talmudist Rabbah on Taanit 25b says that he has seen the angel appointed over rain, Ridia, who he likens to a calf with parted lips.
Geniva quotes Rav Hanan son of Ravah on Gittin 31b, saying that Ben Netz stays the fierce southern wind. Rashi comments that Ben Netz, literally translated as '[Son] of Hawk', is an angel made like a hawk.
The common concept in our current society of an "angel" is that of a person with "feathery" wings. That of a "devil" is that of a person with bat wings and horns. We have the description of the merkava and other descriptions of people with six wings. We also have the description like a person with the legs fused into one pillar. In fact, I have had problems using the term "angel" as too many of us automatically "see" the images from movies, television, or "religious" art in the museums. As a result, I suggest using the term Mal'achim, and avoid any attempt to translate it into English. I have spoken with teachers who have told me that they have had difficulties explaining some concepts when using the term "angel" that did not show up when using the term "mal'ach". This is a practical matter rather than a matter of halacha.
As @Baby Seal points out many "appearances" are metaphorical only. The meforshim of the "men" that visited Avraham (and went to S'dom) explain how three mal'achim came to Avraham and two went to S'dom. Each mal'ach is "created" for its specific task and only "exists" for the duration of that task. This is also the explanation of the reaction when Yaakov (and later Manoach father of Shimshon) asks the name of the mal'ach. The "name" of the mal'ach only exists in relation to its task. Once that task is complete, the name is gone.
Similarly, there were three tasks required in the visit to Avrohom. The mal'ach sent to predict the birth of Yitzchak finished his task and "left". The mal'ach sent to heal Avraham either had the rescue of Lot as part of that task or became "available" for a similar task afterward, or was just replaced by the mal'ach sent to rescue Lot. The third mal'ach, to destroy S'dom, was needed as part of the three, according to many meforshim, because the fate of S'dom was not completely decided until Avrohom showed the real chesed of his acceptance of the three "men".
A mal'ach can be a person, a natural event, or a supernatural being created and sent for a purpose. There are many examples.
A TSA official who delays someone so that he misses a flight he is not supposed to be on.
A woman and child taking the seat of a person, so that he can show chesed by letting them sit together.
A traffic jam to force a person to take a particular route.
A sudden rain or a wind to blow the clouds away.
And of course the mal'achim as we see in the case of Avraham, Yitzchak, and Yaakov as well as all the other times mentioned in Tanach.
Thus there is no specific "image". Additionally, one is not supposed to create images of the "residents" of heaven, but that is another question from the Ten Commandments.