Brooms, as I pointed out in my blog the other day are largely used for symbolism. There is no witch that I know of personally who actually claims to use her broom for physical flight. And its the kind of thing you would boast about isn't it? If I could fly on my broom, I'd take the odd pic, I'd let it slip, I wouldn't be able to keep it quiet!
As to whether its possible, well I'm not so sure I'd rule it out completely. There are documented cases of levitation. But I've never encountered any specifically concerning a broomstick. I suspect that anyone having a mind capable of defying gravity would probably be putting it to better use than joyriding broomsticks.
So I'm sorry if I've disappointed you. Brooms are a traditional heritage with plenty of modern meaning for the witch of today. But sadly our transport is buses and trains, same as anyone else.