In many cultures, 7 is considered a number of completeness or perfection, and it appears frequently in religious and cultural contexts. Additionally, the number 7 is often used in various forms of media and entertainment, which may contribute to its popularity as a "random" choice.
The most popular picks are in fact 69, 77 and 7 (in descending order). It's well known amongst purveyors of conjuring tricks and the like that if you ask people to pick a number between 1 and 10, far more people choose 7 than any other number.