Yes, there are a lot of slimy foods in Japan. I particularly do not like slimy food, but Natto (納豆) I can handle Natto no problem, but some other slimy Japanese food is not my cup of tea...　 There are few other common slimy items in Japanese food:

Sea urchin (Uni, うに):
This is also popular item in Sushi restaurants in the U.S. But wondering how many people know what part of sea urchin is eaten as sushi or sashimi? It is ovary and testis of sea urchin, yes, that is where sliminess of sea urchin comes from. At high end sushi restaurants sea urchin is served raw so it is very slimy. Testis only part of sea urchin is valued very highly at high end sushi restaurants and it is priced very high.

At not so high end restaurants often sea urchin is processed (steamed and few other processes) for the shelf life and those are not as slimy as raw sea urchin.

Shirako (白子):
This is also well known slimy white items eaten in Japan. Shirako is ovary of cod fish, angler, or blowfish. Do you start to get the trend? Anything raw and slimy at sushi restaurants…　

Jynnsai (純采):
This is vegetable, water shield grown in ponds or lakes which looks like lotus. Young buds of this vegetable is covered with slimy clear agar substance. It is commonly eaten at northern part, Tohoku region of Japan but not that difficult to come across in Tokyo.

Hata-hata (ハタハタ):
It is sandfish common in Sea of Japan. The fish itself is nothing unusual, just like eating any white meat fish. But one of common way to eat Hata-hata is in hot pot dish, cooked right on the table in broth with vegetables. Well, they usually use female Hata-hata with eggs in the belly. And this egg of Hata-hata is covered with slimy clear liquid stuff. In the hot pot dish Hata-hata is cooked so that egg is still pretty much raw and part of the hot pot dish is to enjoy this sliminess of egg. It just was not for me…

Talk about hot pot dishes. Ankou-nabe (angler hot pot dish, あんこう鍋) and Suppon-nabe (Japanese soft shell turtle hot pot dish, スッポン鍋) are something not difficult at all to find in Tokyo. Both meat of angler and soft shell turtle contains large amount of slimy stuff made out of collagen. It really is slimy, and sorry but it is not for me.