Full Faith and Credit
Official documents, like marriage licenses, divorce papers, birth certificates, and driver's licenses are valid in all states. Article IV of the Constitution requires that states give full faith and credit to the public acts, records, and civil judicial proceedings of every other state. So, payments can cross state lines. Otherwise, people could move to another state to get out of paying their debts. In addition, people would have to get a marriage license in every state, meaning you could be married to one person in New York and be a bachelor in California.
If you commit a crime in another state, that state is required to return you to the state from which you're from. This is called extradition. Although states don't have to do that, they are usually happy to comply, because they don't have to harbor criminals. That's why many countries also extradite people back to their home countries.
Privileges and Immunities
This obligation is the most complicated; it states that states can't discriminate against citizens of other states. For example, if a Texan visits California, he will have to pay the same taxes and will receive the same police protection as residents of California. An exception to this is the tuition of a public university. Students from the state of the public university pay much less for college, while out-of-state students pay much more.