Angels Landing is the famous one. The five-mile round-trip starts on the canyon floor at the Grotto shuttle stop, climbs in switchbacks (Walter's Wiggles, twenty-one of them) to a saddle called Scout Lookout, and then follows a narrow ridge of bare sandstone for half a mile, sometimes only a few feet wide, with cliffs falling four hundred metres on either side. A chain bolted into the rock provides the only assistance.
The summit views are extraordinary — the full sweep of Zion Canyon, the river below like a green thread, the Great White Throne directly opposite. The hike requires a permit obtained by lottery in advance. Allow four to six hours, do not attempt in wet or icy conditions, and seriously reconsider if you are afraid of heights.