I'm an avid runner. Usually 5 or more miles per session. I ran with my EVO all last summer using the arm bands linked to above (post #3). They look a bit hokey, and are a bit of a tight fit, but they do work. And with all the varying form factors that smart phones come in, this is probably the best we'll see.
I wouldn't worry about any 'extra stress' on the device. If it's mounted on your arm, it's seeing very little stress. I wouldn't mount in on your waist. No because the impacts might damage the device (there than shacking a memory card loos), but because the point of attachment will break eventually.
I wouldn't go out in the rain with it, though. Moisture is the enemy of electronics.