Can you go to an Apple store for a problem with a product you bought in another country?

I got an iPhone in Germany, but I'm in Japan now. The camera has got some issues, and I wonder if I can go to a Japanese apple store with my problem or do I have to wait until I'm visiting Europe/Germany the next time?

Absolutely go to an Apple retail store if one is convenient. Worst case, they can assist you in setting up service in the country of origin if that is needed, but in many cases, parts are universal should you need an actual hardware repair.

Both countries you mention also have web service, so you can set up service and possibly a repair without needing a trip to the store.

Technically, Apple could ask you to mail the product back to the country where you bought it, but my experience is that is reserved for rare circumstances and not the normal procedure.