gunmajet.net

This is a list of train schedule search sites. They are all similar, but differ enough that you might want to try them all. If you have a mobile plan that lets you use the internet, these are incredibly helpful when you are lost and don't know the correct train for home.
hyperdia.com
After entering the starting and ending destinations, you can select what type of train you want to use (express, limited express). This is especially useful for people visiting on the Japan Rail Pass, where you don't want to use the Nozomi Super Express.
jorudan.com
This is similar to hyperdia. It doesn't have as much flexibility for searching for a specific type of train, but it does allow you to search for trains arriving at a specific time. Hyperdia only does departure times.
ekitan.com (Japanese)
This site is good for searching for trains, and works well with mobile phones. However, there may be a ¥105 yen fee for using the service.
Eki-net
In Japanese but useful. You can search by arrival or departure time. Does not give fare info.