This could just as easily be in the "Must See" tip, as some of the trail heads are easily accessible, especially the one just above Wallowa Lake at the end of the road.
Eagle Cap is the largest wilderness area in Oregon with some 350,000 acres, 53 Alpine Lakes and 47 trailheads.
Fill out a wildeness pass before you hike or pack into the wilderness (located at each trailhead) and buy a travelers pass ($3) to park at a trailhead (at USFS center in Enteprise or local businesses).
There is "no trace" camping, what you pack in you pack out. No campfires are allowed in the popular lake basin.
A good book especially for more than day hikes is "Hiking Oregon's Eagle Cap Wilderness," a Falcon Guide by Fred Barstad. The majority of trails are fairly strenous because they all involve moderate to major elevation gains.
Update, Sept. 21, 2005: To see more about hiking in the Eagle Cap please see the Joseph page of mtncorg -- we had a "meet" in my front yard while drinking a Terminal Gravity beer this summer. His page is almost exclusively about the wilderness and has some great photos!
About 30 miles east of Joseph is the little unincorporated town of Imnaha, famous for the Bear and Rattlesnake feed during the annual Canyon Day in September (there's also a parade, tug of war, rodeo playday and outdoor dance). Locals hang out at the Imnaha Store and Tavern.
The paved road ends in Imnaha, though you can go down to Dug Bar, the only place in Oregon you can actually access Hells Canyon by road (about 20 miles, 1 1/2 hours), or up to the Hat Point fire tower overlooking Hells Canyon (not a sissy drive, either.)
Somewhat lost in the drama of the Lake Basin is small Upper Lake, lying just beyond Mirror Lake. The lake is set at the head of the upper East Lostine Valley and serves as the river’s source. You can find a few fish in the lake and there are a few campsites hidden away. The increased isolation and views down the East Lostine more than make up for the more crowded Mirror Lake and its glorious views of Eagle Cap.