Fly fishing vest - A pocket for every fly box. A home for every gadget. Vests are great because they let you carry all the tools you'll need on the water, plus anything else that you may want to store.
Waist Pack or Chest Pack are becoming ever more popular for holding your fly box, tippet and extra tools.
Non-slip Devices - Not only is it no fun falling in the water and getting wet, but doing so in a heavy or even moderate current can be extremely dangerous. Safe wading is happy wading and items like a Wading Staff will help you navigate a slippery stream bottom with confidence.
Fly Boxes - There are many styles of fly boxes available today. It is best to match your fly box to the types of flies they will be storing. Dry flies will do well in a compartmentalized box so that their hackles don't get crushed and foam insert boxes are ideal for keeping wet flies and nymphs sorted and untangled.
Rod & Reel Cases - protect your equipment when not in use.
Landing net - makes it easier to land your fish once it is within reach and helps gently control the fish for easier hook removal and release.
LED headlamp - aids with night fishing and is useful in emergencies.
Insect repellent - just be sure not to get this on your fly line or fly!
Lip balm and sunscreen