I keep a basic kit found in many hotels in my briefcase for "at work" misadventures. For outdoors, I wound some strong nylon thread around a business card (what I had handy at the time and just never got around to replacing) and a carpet (?) needle. The heavy needle is good for getting through nylon webbing. Used it on a backpacking trip to repair a hip belt. This is where having a Leatherman with the needle nose pliers is handy to help pull (or push) the needle through multiple layers of webbing. Repair held for the remainder of the trip.

My backpacking repair kit includes the nylon thread and carpet needle mentioned above, six wire ties, several assorted frame pins & rings, 6 feet of duct tape wound flat around a piece of wax paper, and 50 ft of 1/16" braided nylon cord. Haven't found anything that I couldn't fix yet on the trail.