Check websites like Film Metro, which keep up with advance screening schedules. If there is such a screening in the city you live in, the site can tell you where and when it is and how to get passes. Most of the screenings are first-come, first-serve. For high-interest films, you may need to go an hour or so in advance to get a seat.
Check the websites of upcoming films for announcements on free screenings or promotions. Some films have tie-in promotions with products, media outlets or restaurants that can include tickets. Some DVDs come with "movie money" that can be redeemed with coupon codes and printed out as free movie tickets.
Get work at a movie theater. Most of those jobs come with the perk of free tickets or admission to its movies.