When you receive a traffic violation you're supposed to receive a notice, the ticket is supposed to be copied and filed away, and the government is supposed to keep a watch on your paperwork. However, information might slip through the cracks and it's entirely possible that your traffic violations could get lost somewhere in the system. To err on the side of caution, it's best to check periodically to see if you have any traffic violations if you're not sure.
Go to the homepage of the local courthouse where you think you might have traffic violations. Some courthouses will provide a database of traffic offenses, and you can type in your name and the car's license plate number and registration to search for yourself. If this isn't an option, you'll have to go a little lower-tech.
Call the courthouse and ask to speak to the public records clerk. Because a traffic violation is a public record, much like an arrest or conviction would be, the record should be in its system. The clerk might not be allowed to give the information to you over the phone, however.
Go to the courthouse in person and speak to the records clerk. If you call first, you should get a definite "yes" or "no" on whether you have traffic violations. If you do, you'll need to come and see what they are. You can usually make payments for them right at the window at the courthouse if necessary.