Not only am I a non-swimmer, I have a terrible phobia of drowning. Probably due to:
A college-age cousin who drowned in a scuba-diving competition.
My grandparents living near an irrigation ditch with a huge drop and heavy flow.
Being “taught” to swim at summer camp by being thrown in the deep end.
And, yes, I have flying dreams, and actually enjoy them. I think it’s because I am in control while flying.
I’m a strong swimmer, and I have flying dreams every other night if not every night…
But I’m always upright, not horizontal!
The best ones though are the Lucid Dreams… then I grow myself some wings! 
mmmmm, Big White Feathery Angel Wings…
Now where do I go for surgery?
Yes it’s unusual. It’s one of the most common dream types, up there with falling dreams and suddenly finding yourself embarassingly naked in public. I’ve never had a flying dream (I can swim) ** or** an embarassing public nudity dreams(not embarassing, on the other hand…) Falling dreams, though, I have frequently. I’ve even dreamed that I was trying to catch something that was falling and startled myself awake that way.
It’s weird, I’ve only had a couple of dreams where I was naked in public, but I regularly have dreams where I realize I am in my underwear (and even though I haven’t worn them for years, it’s always plain white briefs). They aren’t particularly embarassing, because in the dream I keep thinking ‘I’m wearing my underwear, it’s not like I’m naked’.
I also have the falling dreams, but they aren’t so much dreams as a feeling I get just as I am about to fall asleep.
I’ve also never had any flying dreams, or public nudity dreams of any sort, at least so far as I can remember. I have had plenty of falling dreams, however.
FTR, I can swim, took years of swimming lessons as a child, but I’ve only been swimming three times in the last three years.
I often have the flying dream. Usually after many non-stop hours of playing first-person shooters, like Counter-Strike.
Also, I have noticed that if I take melatonin as a sleep aid, I have very lucid dreams and I can remember almost all of them. Like there was the one where it was me, the Barbie twins, a trapeze… er… umm… sorry… I digress…
I can swim, but I use too much energy when I do, and therefore don’t like to swim unless I’m in a pool or next to land or a dock.
When I fly in my dreams, I’m upright. But my method of propulsion is unique to what I’ve read here. Imagine me standing there, and by bending my knees, bringing my feet up behind me, pumping my legs like that, I can fly up and forward. It takes alot of energy to fly for me. And I’m always having problems dodging powerlines.
Cecil Adams should really check this thread out. I’d love to know if non-swimmers really did indeed fly vertically in their dreams more than horizontally.
On another interesting note, but not related:
If given some toy blocks to build with, boys will tend to build towers, while girls will build walls.
I think it’s time for this one to go to IMHO.
My flying dreams are fun but the flight is a bit rubbish. It consists of jumping slowly and never quite touching the ground. All I can do is float slowly around, maybe half a foot off the ground.
That’s not unlike my swimming skills. Except I can use my arms when swimming.
Non-swimmer, I have flying dreams often enough. They’re usually more the upright gliding variety though, where long strides lead to controlled skimming some distance above the ground.
To the best of my memory, I’ve never once had a naked-in-public dream.
I don’t swim. I can’t float. My best bet is to sink to the bottom and run to shore as fast as possible.
Having said that, I’ve had flying dreams. Both laying out and standing up. I find I can relax my awareness enough to enjoy a good flight.
Now, Nightmares, OTOH, I don’t have.