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. At the top of the list I would put hip waders and wading boots. If you have waist high waders or chest waders, 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 pofile. Stealth really is the key to fishing a short line and kneeling where possible is a very good way to be stealthy.
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 or a slightly more traditional wooden tamo you could always make your own. 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 from TrailLite designs, the masters of ultralight gear that brought you the Ebira rod quiver.
For your net (or wading staff), to make sure you can use it but not lose it, you'll have a hard time finding a better solution than the Gear Keeper.
You may also want a TenkaraBum Cap to keep the sun out of your eyes, and 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.
You may also want something to carry a lunch, a water bottle, and maybe a light rainjacket. 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.
The Ebira rod quiver is a handy way to carry your rod and gear (and maybe even a second rod), and the small 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. For the true minimalist, the minimalist fly box holds up to three dozen flies and can be worn on a lanyard or a zinger.
Streamside tools (hemostats, nippers, a zinger) and a pair of Fuji EZ Keepers or a tenkara line holder also qualify. However, I really much prefer the Dr Slick Mitten Clamp to regular hemostats. More and more tenkara anglers are replacing their heavy, bulky fishing vests with a minimalist chest pack like the Tippet/Fly Pouch.
To help prevent rod breakage, a Tip Grip is very nice to have. That they're absolutely free makes them even nicer.
The 20/20 Magnetic Tippet Threader will make it easier to thread the tippet through your hook eyes, and 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.
The goal, in my mind, is to balance Thoreau's admonition to "Simplify, simplify" with the benefits of having with you the things that make a day on the stream or the pond more enjoyable. I suppose every angler has his or her own list of tenkara accessories and eveyone's list will be different.