The first type is called "Nobi Nobi Carpet Cars." They are trains full of little bunkbeds made out of wood with carpet on top, and a blanket and pillow are provided. Your taste may vary, but I've found sleeping in these cars very comfortable.

The second type is called "Goron to Shito." I don't know exactly what that means, but basically you get a bunkbed with a mattress, but no pillow or blanket. These are a bit more comfortable that the Nobi Nobi.

There are also overnight trains without beds. These aren't nearly as comfortable as the bunk beds, but the seats usually recline way back. I've slept in one for the past two nights and have had no problems getting a solid night's sleep.

One important point, which I've learned the hard way, is that the beds-classified-as-seats can fill up quickly, so it's best to book them as far in advance as possible. During peak season that can be a few days. In the off season you can get them hours before they leave.

These sleeper trains are very slow, which means that where they end up is almost irrelevant. You can take a Shinkansen bullet train back to wherever you want to go that day.

Whether or not the train has a shower seems to be random, but they all have bathrooms and sink areas to brush your teeth. If yours does have a shower, use it. They're really cool and it's fun to shower in a moving train.

If not, look for an onsen. These are public baths fed by natural hot springs. You'll never feel more clean or relaxed after visiting one, and they're a great part of Japanese culture to enjoy. They range in cost from a few dollars for a small one tub onsen to more that twenty dollars for a more elaborate one.

Japan-Guide has a great overview of the night trains which is a pretty complete list of the loophole cars. I found at least one not listed that was also a nobi nobi.