There's a lot of factors involved for me when it comes to deciding how often to stop.
Time: If I have all day to go 200 miles, and nothing else to do that day, I'll probably use most of it and take my time getting there.
Weather: Crappy weather means more stops. Once you realize you're too cold, you're already hypothermic.
Knees: I've got fucked up knees, and being 6'3 doesn't help. Even a proper sport-touring bike is still a bit cramped for me. Some days it's fine and I can make a 500 mile ride only stopping for gas, and some days I feel like I'm going to die after just an hour of riding.
The route: Most people don't think about this one. Riding the big, wide, straight freeways is more draining than riding a gently winding back road. On the freeway you don't move much. As Neil said you're sitting in the same odd position for hours on end. On a back road that has corners you'll move around a bit and your body will thank you. I can ride the mountain twisties for 8-12hrs and feel just fine when I get home, but 2hrs on the freeway leaves me reaching for the tylenol.
Mood: Sometimes as the end of a trip nears you either don't want it to end, or you just want to be there already. If you're tired of being away then stopping more often will make it feel dragged out and miserable. If you don't want it to end then stopping more often can be better as it prolongs things a bit more.
Case in point: In late November I took a ride up to Kentucky to visit an old friend of mine. The town we were meeting at is only about 250 miles away, which really isn't very far for me. Took the back roads, and the moving portion of the trip should have been about 6hrs. Going up there I only stopped twice. They were somewhat lengthy stops, but it still only took 7hrs. Coming back home the weather was not on my side and I had a couple small problems with gear. I ended up stopping 5 times just to get off and walk around a little. The return trip was the exact same route and it took a little over 8hrs.