Because Japan lies where three tectonic plates meet, it has around 1,500 earthquakes every year and multiple minor earthquakes every day. When bad enough earthquakes happen, tsunamis can make matters worse. The word “tsunami” itself is a Japanese word, combining the characters for “harbor” and “waves.”
Because of the tectonic plates, there also are a lot of volcanoes. Mt. Fuji, Japan's most famous mountain that can be seen from Tokyo on a clear day, is an active volcano. It last erupted in 1707, but there is always the possibility it could erupt again. Typhoons (basically hurricanes but in the Pacific) often hit Japan as they come up from the South Pacific. The only major natural disaster that does not often occur in Japan are tornadoes.
Another challenge they face is humidity and mild climate. In most of Japan, the temperature never gets too cold or too warm, so it has the ideal conditions for mold to grow all year round. I don't think the humidity in Akita has dropped below 65% the whole time I've been here.
The mountainous areas also creates another challenge in this environment. Only 15% of the land is suitable for agriculture, which means that is about the only land suitable for living.
So how do the Japanese people deal with all of this? For earthquakes, they have made some amazing technology to reduce how much buildings sway, preventing buildings from being critically damaged even in catastrophic earthquakes.
