The steepest trail I've hiked is the climb out of Cotahuasi canyon in Peru with ~1600m/5248ft of elevation gain over 7.8km. It was eye-wateringly steep, especially at the beginning and near the end, and HOT. There was a small creek, but it was difficult to access so my wife and I carried 5L of water between the two of us. Our mistake was not starting the hike at 4am...
The steepest trail I've "run" on was just this weekend at the Salomon X-Trail half-marathon in Breitnau, Germany. 750m of elevation gain, two huge descents. A portion of the climb out of the Höllental (Hell Valley) was so steep that I didn't see anyone even trying to run. I was so toast that even just walking up was difficult, and I'm still sore 3 days later.