State laws differ on how long a violation, whether points are associated with it or not, will remain on your driving record.
So for instance if in the state you live in you receive a speeding ticket for under 10 mph over the posted speed limit and are convicted of the charge but are not assigned points the violation will still go on your driving record normally. The violation will then stay on your motor vehicle record (MVR) for a time period set by your state's laws or statutes.
In general, states usually allow for moving violations or tickets to stay on your record for 3, 5 or 7 years. If the violation was more serious, for something such as driving under the influence, states typically keep this offense on your record for a longer period of time. Some states keep all violations on your driver's history for life.
To get a definitive answer of how long a ticket stays on your license in your state or for information about this law in other states, contact the Department of Motor Vehicles in each area.