Some homes will have well water instead of public water, you should have the well inspected
In a lot of older homes lead is still a problem. It's a good idea to have the house inspected for lead and in some cases it's required so ask your inspector.
Radon is a very dangerous and odorless gas that comes from the ground below. Some parts of the country have a high concentration level. Radon is known to cause cancer. Ask your home inspector about Radon levels in the area that you plan to live in.
Mold can be a hazard to you and your family's health. This type of inspection looks for the presence or evidence of any mold.
Some homes have their own septic system instead of public sewage. In this case it's a good idea to have the septic system inspected.
Termites are wood destroyers and can eat up a home. Get the house inspected for termites before you have a major problem.