I don't leave home without one of my Xped sleeping pads (summer or winter version) b/c it is the most comfortable I have personally found. It allows a good night rest for those 20+ mile days.
The one thing that I never leave behind is a knife. At the very least, a sturdy EDC pocket knife; or a small fixed-blade bushcrafter knife. To paraphrase @Tetons2 , it is just so versatile! I've used mine for everything from splitting campfire wood to carving up a freshly picked paw-paw for an on-trail snack!
(can you have many items as favorite?) Anyway...if my air mattress blows, trip is over for me! I need to stay warm and dry...and recommend not leaving the trailhead without the "ten essentials"!
Besides the essentials and my trusty trekking poles, three pieces of gear I've used the past couple of years that I'll NEVER backpack without are (two are girl-specific, so sorry guys):
Whether it be an ultralight foam pad, or my REI Flexlite chair I never leave home without something to sit on!
"From the highest king, to the lowest peasant...everyone enjoys a good sit."