Scrubbing back-and-forth or in circles probably aren't the best ways to brush — but those are the most popular methods taught to kids and endorsed by toothpaste companies. Dentists, on the other hand, tend to prefer something called the Modified Bass technique.
To brush your teeth this way, angle your brush at the gumline, move it in a circular motion to loosen plaque at and underneath your gums, then sweep the brush away from the gums to remove debris.
Optimal tooth brushing isn't totally agreed upon: an analysis published in the British Dental Journal found plenty of disagreement about how long, how often, and what techniques were best. Of ten dental associations that recommended a specific technique, six preferred Modified Bass because there is some evidence that it may be better than other methods. That method was rarely taught to children, though, so consider the Modified Bass tooth brushing technique one of the better kept secrets of adulthood.
Brushing Techniques Modified Bass [Columbia College Calgary (Youtube)]