Alot of vegans and vegetarians experience alot of problems conveying to restaurant staff what being a vegan or vegetarian means. Simply saying that you are vegetarian is usually understood to mean not eating cow and in some rare cases chicken or pig, but never fish. The word for vegan is very long and many people don't understand it unless they see it written and don't understand what it entails so it is much better to explain that you do not eat animals or animal products and give a list of examples. Even doing this though isn't always successful, even when you have Japanese friends with you to help out with the explaining.
I have been caught out a few times. The most memorable experience is when travelling in Wakayama with my lovely flatmate and after informing the host that I didn't eat animals she decided to conceal the meat at the bottom of the plate and cover it with noodles. I was not impressed but remained surprisingly calm.
In Japan there are a number of very common restaurants and eateries which might seem ok for vegans but are not. Here are the most common ones:
Okonomiyaki ?????
These places are everywhere and serve noodle stir-fries (yakisoba - ???? - and yakiudon - ??????) and savoury pancake things (okonomiyaki - ?????). While they can make food with just vegies they always use lard. You can probably ask the cook not to but don't expect people to agree.
Udon ???, Soba ??, and ramen ????
These places sell noodle soups. While ramen uses pork stock, udon & soba soups are always made with fish stock. In almost all cases this won't be negotiable.
Izakaya
Izakaya's are usually described as Japanese style pubs where you can eat and drink. There is often a picture menu and there are usually things that are okay to eat but its a good idea to quiz the staff about oils, hidden ingredients etc..