I was going to put a sloping roof (just out of that corrugated plastic roofing material, cheap at Lowe's or Home Depot), but by the time we finished the run, I was exhausted! We put up a large tarp covering just half of the run, and it looks like it might be the permanent-ish solution. So far we've had a good bit of rain, and most of it runs off (we have the run covered with hardware cloth of course). The water does pool a little, but I'm not worried. I've seen some runs on BYC that have tarps as roofing.
Some sort of roofing is crucial for the run. I keep some of their food and water out in the run since our coop is so small, so I like to have the protection of the roof to keep all that stuff dry and fresh. I also look forward to a winter snow where the girls can still go outside and stretch their wings. The tend to stick to the dry shaded sand after a rain. So in conclusion - some sort of cover is necessary!