At the very least you should carry something that cuts, and something that pinches. (And no, your teeth and fingers don’t check these boxes). Nippers or a pair of forceps with a cutting surface are essential for cutting off tag ends of tippet and removing lengths of tippet from the spool. Forceps (or clamps, hemostats or pliers) are essential for pinching barbs and making quicker work of removing hooks from fish.
Beyond these two things, there are a few items that we recommend to help you have your best day on the water:
Floatant/Sinket: dry flies don’t always float the way we’d like, and nymphs don’t always sink as fast as we want them to. Carrying a floatant for dry fly fishing and some Tin Drops or Deep Soft Weight for nymphing is essential for getting the most out of your day on the water.
Zinger: ideal for keeping tools accessible but out of the way.
Tippet Post: ideal for keeping spools of tippet stored together.