I've carried a tiny sewing kit for years. When you need it, you need it, and nothing else will do.

My outdoor trip kit is dirt simple: three fine needles, two heavy-duty needles, a "holder" made of a Papermate pen and cap that I cut down to size, wrapped with a heavy-duty poly/cotton thread on the outside and held on with an elastic band. It weighs a fraction of an ounce, so it never gets left behind.

With this crude kit, I have made critical repairs to pack straps, fixed zippers on sleeping bags, tacked a nylon "slider" into the heels of a novice hiker's boot (reduces friction/blisters) and etc. The cap serves as a thimble, sort of, but I much prefer needle nose pliers or a multitool (as others have wisely noted).

I also carry a few diaper safety pins (all metal) with my kit. Amazing what you can fix and improvise with these.

BTW: Ten years later, my repairs are holding. When I sew something, dammit, it stays sewn.