Here is a list of websites to get passes for early screenings of upcoming movies before they are released nation wide. These websites are most or all for United States of America screenings and you have to sign up for them all.
Gofobo
Sending pass for movies of all types mainly for up to 2 guests, sometimes 4 for kids movies. More movies you go to the more movie passes you should get. You can get flooded with passes for the same movie but for different times and places to watch it. Many time I get dry spells of no passes at all for 2-4 months.
Sony Screenings
Like Gofobo in the pass guest count and how often passes are sent but only shows SONY movies.
Regal Entertainment Group
Regal may send out a free pass in their newsletters. I forget if you have to also have to be a member to their free members club too. I got one pass from them so far and the passes will be for a screening in a Regal theater.
The Film Yap
The Film Yap is a local movie reviewer/lover website. Many times they will post on their website, newsletter, and/or FaceBook page of mini contests to win passes to an early screening.
Nuvo
The free weekly Indianapolis paper has many contests on their website. Many of which are for passes to early screenings.
Local comic shops
Local comic shop tend to get passes to comic/sci-fi movies. Some will just hand them out, other times you'll have to call in before hand, you may have to buy something some of the other times, and there is even a chance they will have a contest for the passes with other goodies. Be sure to check their websites/Facebook pages/newsletters for updates and don't be afraid to ask.
Lionsgate
Just like the SONY screenings but with Lionsgate films.
Warner Bros. Screenings
Just like SONY and Lionsgate but with WB films.
I think there was a Paramount screening site too but I can't find it.
Get Screening
This site I haven't used just yet but I hear it's like a blanket site that sends you passes from most of the other sites I talked about above.
