I can't swim for shit... I took lessons and still can't float that well. That was when I was a bit fatter too. Now I'm 5'8 with about 11% body fat and I weigh 175lbs so I'm pretty certain it's lot more difficult now than it was before.
Some people can float on their back without moving their arms/legs... I just can't do it. I've had my instructor place their hands under my lower back to keep me up but as soon as they let go, my legs just trail back into the water until I'm upright. I just don't know what it is, I just can't keep my legs up when I lie on my back calm and relaxed. If I kick my legs though, I could stay afloat for as long as I'm doing it.
edit: I also have a very difficult time keeping water from going up my nose when underwater on my back. I just don't know how to close the passageway.