Anybody who has ever caught a bus knows it fills up to a silent dance. Empty rows are filled one by one until the wary person walking up the aisle is forced to sit down next to someone else - and then only with a desperate, neck-craning final check of the seats. The same basic principle applies to the beach - on a crowded day, put down your towel in the spot that will put maximum distance between you and others.
Proxemics - the study of measurable distances between people as they interact - shows that different cultures maintain different standards of personal space. In Latin cultures, for instance, people tend to be more comfortable standing close to each other. New Zealanders are a more reserved bunch, so on all but a deserted beach aim for at least 10m between you and others.
Variables play an important role - are you a young man and the stranger is in a bikini? Are you carrying pamphlets warning of eternal damnation? Are you a teenager playing Soulja Boy through tinny speakers? Do you have baggy jeans and a pitbull on a straining leash? Add a few metres.