Each insurance carrier used a different formula for defining "new drivers." For some car insurance companies, drivers are considered "new" until they have three years of experience on the road, for others it can up to five or nine years.
Some carriers do not look at the date that you were first licensed, but instead use your age as the only determining factor. In this case, typically that means you are deemed an inexperienced or "new driver" until age 25.
Typically, an insurance company will charge you more after an accident for three years after the date of the incident. State laws vary, however, on this issue, so in some cases it can be as long as five or seven years. Usually major infractions, such as a DUI, remain on your driving report longer than a fender bender.
If your rates are too high due to being a new driver that has been in an accident or convicted of DUI, read "How high-risk drivers can get lower car insurance rates" for tips on how to save money on car insurance.