Generally speaking, in most states, the answer is yes. Since all states have different rules, and in some states it even depends on the county or city you live in, always check with your local building department, I'm sure they'd be glad to answer your questions. I would love to someday compile a list of each state and area and have that info here, but it is a huge project to go state by state, county by county, city by city, and so forth researching the local laws!
Always get a permit! Contrary to popular belief,
permitting agencies and inspectors are not just out to get you. Most
inspectors are more than happy to help you get through your project
efficiently and safely. Permits and inspections protect everyone. If
you have done something incorrectly or unsafe, an inspectors job is to
catch that mistake before anybody gets hurt by it. One more good reason
for a permit: if something happens to your house (fire, flood, tree
falls on it, whatever) and your homeowners insurance company finds out
you did work on it without a permit and inspections, you'll get no
money from them!