Tenkara accessories are all those things (beyond your rod, line and fly) that you may not actually need, but they do come in very handy.
I am often asked, "What do I need to start tenkara fishing?" Besides the rod and the line, you will need a way to manage the line when the rod is collapsed. I would recommend either the Tenkara Line Holders or the Fuji EZ Keepers. The EZ Keepers are a little more convenient, but the Tenkara Line Holders allow you to store the line when it is off the rod, and you can store it with the tippet and fly still attached. I recommend getting two so you can have lines of different lengths.
Streamside tools (hemostats, nippers, a zinger) will be necessary if you don't already have them.
I would also highly recommend a tenkara net, either the ultra light, ultra strong Ti Tenkara net, from TrailLite Designs, the collapsible Shimano Folding Net. If you enjoy making things yourself, a more traditional wooden "tamo" is an interesting project. If you have a net or a wading staff, and I would recommend fishing with both, you will want something to tether them so you can drop them when unhooking a fish or taking a photo and not have them float away. I really like the Gear Keeper for that. It's like a zinger on steroids.
And after you've netted the fish? In some circles, catch and release has become little short of a religion. I am not a religious person. If you are backpacking and hoping for a fish dinner to supplement your freeze dried food (or if you are not backing and just happen to enjoy a fresh fish dinner from time to time), you will need a way to carry your catch. You could do a lot worse than the Tenkara creel. Even if you don't keep fish, you may want something to carry a lunch, a water bottle, and maybe a light rain jacket. In that case, the TrailLite Designs StreamPack is just the right size. If you also need to carry a pair of rolled up hippers, and a few more odds and ends, the Fishing Backpack would be more appropriate.
More and more tenkara anglers are replacing their heavy, bulky fishing vests with a minimalist chest pack (or over the shoulder, hip pack) like the Tippet/Fly Pouch.
The Fuji Rod Caps are nice as a backup tip cap or as a replacement for the cap that came with you rod. They hold securely and are large enough that they are hard to lose. Replacement lillian is also a backup that you'll hopefully never need, but it is better to have it and not need it than need it and not have it.
The monoMASTER neatly and simply solves the problem of what to do with your used tippet material. I've always wrapped it into a ball and stuck it into my pocket, but sadly there have been times it fell out and floated away. The monoMASTER really is a better solution.
You'll need a cap or wide-brimmed hat to keep the sun out of your eyes, and it is very nice to have a clip-on Hatlight Plus for after the sun has gone down.
Personally, I do not even step into the water without a wading staff. The most convenient may be a folding staff like the Folstaf wading staff or Simms wading staff, but you can also make your own from a broomstick or shovel handle purchased for just a few dollars at a hardware or home improvement store.
If you have more than one fly, you will need a case to carry them. The C&F Light Weight Fly Case is a very light weight and convenient way to carry your flies. The C&F 1544
is also a great choice for tenkara anglers. It will hold all the flies
you need with room for the sakasa kebari forward sweeping hackles. The C&F Chest Patch Threader holds your flies and includes a threader so you can still change them when the light gets low. The EasyGrip™ Foam
Fly Box holds flies securely without damaging the foam. It fits in your pocket or the Tippet/Fly Pouch. And back by popular demand, the ultra light backpackers' favorite, the small Morell fly box. For the true minimalist, the minimalist fly box holds up to three dozen flies and can be worn on a lanyard or a zinger.
Most of the people coming to tenkara are already fly fishermen, so most will already have waders and wading boots. Whether you are new to fly fishing or just new to tenkara, for fishing the small streams where tenkara really shines, consider a pair of hip waders. If you don't already have pair, you will need wading boots. You might want to consider a pair of the wader gaiters that Dr. Ishgaki wears. They protect your expensive waders (and your knees) when kneeling to keep a low profile. Stealth really is the key to fishing a short line and kneeling where possible is a very good way to be stealthy.