Seriously. I grew up believing angels had wings.

Angels with wings--a popular conception, hence part of our iconography, but stemming from the radiation of force from what humans would perceive as their shoulder centers (chakras). It's a case of people pressing subtle phenomena into recognizable forms. Actually, it's said, angels don't even have bodies (humanlike ones), but human perception imposes this form on them. Animals, again it's said, would perceive them as fellow animals--the colonizing power of perception. These beings are said to be part of another evolution, the devic evolution, paralleling humans on this planet. (Birds--with wings!--are also of this other evolution)...

You may laugh at this in ridicule, but are you sure it's not the laughter of the flat-earthers at the idea of sailing around the world? What if (or better, when) "science" discovers another stream of conscious evolution...and that there is nothing "inert" but every form has a corresponding consciousness...? Why should our forms be the only ones that mysteriously have consciousness?

"Angelic or devic evolution

"They are beings on a line of evolution outside and parallel to human evolution. Most are subhuman and others are equivalent to human or superhuman. They are also referred to as daughters of feeling and evolve through the evolution of feeling or sensory nature whereas humans evolve through development of the mind and the experience of pain. It is said that angels work in a direct healing and protective relationship to humanity. It is thought that humanity and other living beings receive much aid and sustenance from devic or angelic evolution without the knowledge of humanity. This help is likely to increase in the future. Fairies are members of angelic evolution. They are normally not visible to the naked eye and are made of etheric physical matter.

"Nature spirits are all the living beings outside the human and animal evolution. Every inanimate object and living thing whether it is occurring naturally or man made has a spirit associated with it. Things such as your car, your house and other manmade objects and natural things such as trees, streams and stones have their own nature spirit. It may be possible to communicate with them and there by improve the performance of your car or other manmade machine." (http://www.einterface.net/gamini/angels.html)

Certain angels DO HAVE WINGS. The Cherubim and Seraphim are winged. Others do not. Only TSCC requires absolutely no wings in art. The concept of wings came from the Jewish temple. Angels are most often shown as female while in the Bible they were usually in the form of men. BTW, how many angels can dance on the head of a pin?

Angels can also be present but not visible.

Fairies have wings, so I guess angels can too!

Because angels don't exist.

Some do, but mormon ones don't. And they're more modest, too.

(Posting again, because it shows the mormon mindset)
http://www.dovesandserpents.org/wp/2012/05/on-immodest-angels/

Because when men invented Angels no one could imagine the concept of travel through time and space and so they used birds as their model. Now we know that Angels can beam themselves around from Kolob to Earth to wherever on Celestial power and having wings is a ridiculous concept. Thank goodness for a modern day prophet.

My Angel doesn't have wings.

She is a nurse in intensive care and is about as angelic as it's possible to be.

Because they're imaginary.
As in not real.

Imaginary things don't actually "have" ANYTHING -- including wings :)

We most certainly do have wings! *cough*

I have not ha the pleasure of meeting an angel, that I can recall. I can, therefor, not confirm definitely one way or the other. I do, however, know some of the symbolism. Allow me to add mine to the accumulating collection of theories.

In LDS theology, angels are resurrected humans, and, if I recall all my obscure arcane correctly, they are all humans from this earth (as opposed to other planets), who have dealings, primarily, with their own descendants or relevant parties thereto. Thus, angels cannot have wings, because they are people like we are. Just regular, immortal, shiny people.

Symbolically, there are three qualities traditionally attributed to beings with absolutes of particular powers:

HORNS: omnipotence, or authority---like nature's crown
Once upon a time, horns didn't appear evil (think about it; only herbivores have horns...not all that scary. Do demons also chew their cud?) Ephraim pushing the tribes together (Genesis and throughout Isaiah) used horns as good symbols of strength.
EYES: omniscience, or extreme knowledge/enlightenment
Pretty much all Eastern religions talk of a third, inner eye. Eyes are attributed to the beasts (angel beasts, not the 666 beast) in the book of revelation).
WINGS: omnipresence, or just speed. Often the number of wings is numerologically or otherwise significant. The aforementioned beasts have 6 each, as do ...cherubim, if I recall: twain to cover the feet, twain the face, and twain to fly.

...those are some complicated back muscles.

The symbolism is no indicative of actual wings, horns, not eyes. That is not to say that the symbolic quality of a third limb girdle with wings on it means a necessary lack thereof. Should such beings exist, they may very well have wings, or horns, or beaks for all I know.

There are my two cents. Don't spend them all in one place.