For the most part I work perfectly horizontal, sometimes at a 0-20 degree angle depending on the painting or the wash I want. I used to incline the paper a lot more, but the watercolor just ended up running where I didn't want it to go. This doesn't apply to when I'm rotating the paper board in general to get certain washes to dry the way I want them to.
Depending on the size of the painting, I have different inclinations. If it's a large work, I'll try to have it vertical (occasionally, if not at all times), so I can get a better view of it. Painting from an angle (laying the paper flat) would create distorted perspective/anatomy. On the other hand, small works like 5" squares are fine flat because I can easily get a good look just by looking down.
Right, um - I think I misinterpreted the poll. I keep paper perfectly flat on a table when painting. If I'm sketching or doodling with watercolour, it doesn't matter as much, but when I am "serious-painting" I keep it flat because I use a lot of water and tricks that wouldn't work if the paper were tilted.
I rotate it very randomly. Some things seem to be easier to do from certain angles, even if that means turning the whole thing upside down. There was one huge painting that I had to tape to my desk because I couldn't keep it stretched otherwise. It was quite annoying not to be able to rotate it at first.