Basically, as long as your brush isn't sopping wet, you can leave it hanging or standing any way you want. Someone did an experiment here a while ago weighing brushes after use, and came to the conclusion that it didn't make the slightest difference which way you store them.
Sounds reasonable. I have used both methods, but prefer hanging my brush. I figure if there is a weak spot in the seal, water has a better chance of seeping in with the brush on it's end. And, since my prime brush has a wooden handle, I prefer the water not drip down on the handle. Does it make a difference? Dunno, I'd have to look at the data (as well as the methodology)--I don't believe the conclusions I read for the most part. Random personal experience is mostly BS, when it comes to proving disproving any particular conjecture. And for about $5 for a cheap stand (I got mine free with the brush) why not?
Then, of course, there are those who do leave their brushes soaking wet. But that's another story entirely.