Everyone has a vice--something that helps them cope, allows them to indulge their shadow nature or make sense of the world. Whether it's sex, gambling, drugs, food, work or exercise, too much of a good thing can be very, very bad. Religious fanatics are addicts in a sense, obsessing over religious texts and using concepts like heaven and hell to ease their fears about death. Fitness fanatics who are addicted to the "runner's high" and put their bodies under enormous stress by running 5 miles in -20 degree weather every morning are every bit as neurotic as those who take drugs to achieve a high.
So to answer your question about what sober people do to pass the time, I'd imagine they engage in some other vice, like pornography, masturbation, religious study, gambling, over-exercising, binge eating/anorexia, surfing the web, playing video games, working or cleaning excessively.
...but I don't know many people who truly abstain from all mind-altering substances (including caffeine, alcohol, tobacco, etc.)