Angels Landing is a short route to a spectacular view point in the heart of Zion National Park in southwestern Utah. It is about 5 miles round trip, with 1500 feet of elevation gain.
www.zionnational-park.com says this about Angels Landing:
The Angels Landing Trail is one of the most famous and thrilling hikes in the national park system. Zion's pride and joy runs along a narrow rock fin with dizzying drop-offs on both sides. The trail culminates at a lofty perch, boasting magnificent views in every direction. Rarely is such an intimidating path so frequented by hikers. One would think that this narrow ridge with deep chasms on each of its flanks would allure only the most intrepid of hikers. Climbers scale its big wall; hikers pull themselves up by chains and sightseers stand in awe at its stunning nobility. The towering monolith is one of the most recognizable landmarks in the Southwest.
Buzz Burrell has summed it up nicely, calling Angel's Landing "The best short hike in the world."
Besides the FKTs listed here, some other fast times are listed on Bill Wright's site.