Tweezers are my personal must-have that I think get overlooked way too often. Anyone who’s ever had a splinter or a thorn stuck in deep, especially out in the woods, knows how quickly a tiny thing can turn into a painful (or even infected) mess. Forget the ones that come in most first aid kits—they're usually terrible. Paying a little more for a decent pair is totally worth it.
Also, I always stash a little tube of antibiotic ointment. Cuts and scrapes happen, and without some way to stop infection, things can get dicey fast. As for those compact sewing kits, I’ve had mixed experiences. The needles are usually fine, but the thread quality varies a lot—sometimes it breaks way too easily. I keep some dental floss in mine, works for heavy-duty stitches or makeshift repairs.