Snorers are often told to sleep on their sides rather than on their backs. This is because if you are lying on your side, the base of your tongue will not collapse into the back of your throat, obstructing breathing.
However, for some snorers, changing sleep position may not make a difference. There are two types of snorers -- those who snore when sleeping on their backs, and those who snore in every position.
According to the New York Times:
"... [W]eight plays a major role. In one large study, published in 1997, patients who snored or had breathing abnormalities only while sleeping on their backs were typically thinner, while their nonpositional counterparts usually were heavier ... But that study also found that patients who were overweight saw reductions in the severity of their apnea when they lost weight."