Ah, I remember going to the movies. I recall those years fondly, before I had kids and an HDTV and a Whirley Pop.
If, unlike me, you go to a theater to consume movies and popcorn, you might want to check out Movie Cron. At this site, you can watch trailers and should you provide an e-mail and create an account, you can have the site e-mail or text you reminders for movie premieres. The site needs a little work, but the important tool of transmitting reminders does work.
The site lets you browse by Top Movies (for the week, month, year, or from the beginning of time) or Upcoming Movies, but both feature many of the same titles. And there are many movies on the Upcoming Movies list that have already been released. Meanwhile, browsing by Genre will get you sorely outdated lists. Obviously, some work needs to be done to the way the site catalogs movies. Stick to the Upcoming Movies list is my suggestion.
For most titles, you'll find a blue Watch Trailer button, which pops up a small video player. For all titles, whether or not the premiere has come and gone, you'll find a green Add Notification button. It pops up a form you can fill out to receive an e-mail or text reminder. You can set reminders to arrive the day of the film's release, two days before, a week before, a month before, or you can set a custom date. You can also set the time of delivery and have a link to Fandango included. After filling out the form, scroll down and click the blue Create Notification button.
You can view all of your reminders via a link at the top of the site. In my brief testing, I received e-mail and text notifications roughly as I had scheduled them.
Note: This post was updated to reflect recent improvements made to Movie Cron's notification system.