You never know when you'll have to measure something, even if it's just for a shopping trip to know what size rug to buy.
Earthquake proofing your space may include screwing things into place. However, be sure to check with whoever is in charge of your housing before putting any screws in the wall.
These will come in handy, I'm sure of it.
Not always for putting a nail in the wall, but always a good thing to have in your tool box.
The thing you bought might not always come with them...or maybe you need to replace one!
Having different types of tape on hand is important for quick fixes when you can't get a professional there right away.
Duct tape fixes everything.
For packages and so much more.
It's important to have a straight line when measuring and marking.
Wood glue, super glue, maybe even hot glue. Having a variety of glues in your tool kit can really come in handy.
This is a general list of terms related to your house which can be used in describing a problem.
Here's a brief list of helpful Japanese you can use when something in your apartment is broken.