For years, I believed—erroneously—that the only right way to clean mushrooms was to wipe them, one at a time, with a damp paper towel. I am very happy to tell you that you can ditch that time-suck and rinse or immerse them in cold water. They will not become waterlogged in the brief time it takes to clean them, not will you "wash away" their flavor. Clean mushrooms just before cooking. If they will be served raw (say, in a salad) you will need to carefully pat them dry.
For a collection of mushroom recipes, see 7 Ways with Mushrooms.
Recipe: Garlic-Stuffed Mushrooms