Japan Rail Pass will cover almost all JR lines including Shinkansen. This pass is pretty expensive so most people get it only if they plan on taking Shinkansen, and the travel on local JR lines are gravy on top.

For travel on private rail or subway lines, I would pay as you go with cash or a debit IC card like Suica or Pasmo. Some of the subways have daily passes but the price can be pretty high. Whether you can save money using the pass will depend on your travel plans.