There are over 100 campgrounds scattered throughout the Mount Hood National Forest. Those at higher elevations are, by virtue of the north Oregon Cascades' generous snows, often closed until mid-summer. These Forest Service campgrounds vary greatly in services, size and charge. Some are reservable; check out Recreation.gov for details and to make reservations.
Much of the national forest is open to dispersed backcountry camping (at a limit of 14 days consecutively and/or 28 days annually). Check at a ranger station for details on areas closed to such activities, which, where allowed, offer immense solitude in the area's more remote corners---from high summit to deep canyon jungle. Make camp 100 feet from established routes and twice that from waterways; stay aware of campfire regulations depending on conditions; and avoid fragile environments like alpine meadows. As always, practice leave-no-trace ethics and filter water for cooking and drinking.
There are four rental facilities available on the Mount Hood National Forest: three lookout towers---Clear Lake, Fivemile Butte and Flat Point---and the Clackamas Lake Historic Ranger Cabin. Clear Lake and Flag Point lookouts are only open in the winter; Clackamas Lake may be rented any season except winter; and Fivemile Butte is available year-round. Check out the Forest Service's "Recreation Rentals of the Pacific Northwest" at FS.fed.us for more information (see Resources).
Off the national forest, there are plenty of nearby commercial resorts, state and county campgrounds, and other facilities for camping. Refer to local maps or county chamber of commerce information.