Zion National Park
It has a strenuous vertical climb in a section called Walters Wiggles, where you ascend a rapid set of 21 switchbacks to reach the main ridge at Scouts lookout. The real challenge though is the final half-mile along the knife edge rim. A nerve wracking climb where you hold onto anchored chains as you hike; the trail is barely a few feet wide with sheer drop-off cliffs on both sides.
At the end you are rewarded with spectacular views of the Zion valley from the 1,500 ft ridge surging out of the valley floor.