I'm a strict vegetarian travelling to Asia (mostly Japan).
Which traditional Japanese foods are safe to eat vegetarian or easy to substitute to be so?
What are common non-vegetarian ingredients to look out for?
One of the biggest traps in japanese cusine is dashi, a stock used in many preparations, and traditionally made from steeping kombu (vegan), grated dried fish (not vegan), and sometimes mushrooms (vegan). It would be typically used in a miso soup, other soups, sushi pieces that do not incorporate any other fish, condiments...
I wasn't in Japan but in nearby countries The hardest ingredient to avoid was fish-sauce, followed by shrimp-paste. It feels like they use it everywhere (but that's not true).
As a substitute I normally use soy-sauce which is almost always available. I could normally make people understand to use it for my food in restaurants.
Vegetarian restaurants and vegetarian food are, I think for religious reasons, not that uncommon in many Asian countries. Also Indian restaurants are mostly aware and helpful with vegetarian food.
I also recommend learning how to say "vegetarian" in the local language.