If you want to catch a movie while in Taipei, Shi Men Ding is the place to go. There are several theaters there within a four-block radius, including theaters that show blockbusters and theaters that show more artsy types of films. We almost never checked the theater listings before going there—if the theater we went to first wasn't showing the movie we wanted to see within an hour, the one down the street probably was! You can wander around the area and will stumble on a movie theater, or I believe the MRT maps will show the locations of some of them (even in English). As in the US, matinees are cheaper, but the first showing of the day (usually around 11am) is cheaper yet. Different than in the US, seats are assigned in movie theaters... so check your ticket (sometimes they just write it on the back—row first, then seat number).
Two things about going to the movies in Taiwan (for us English speakers):
1. Unfortunately, you can't appreciate the many Chinese or other Asian films shown because (of course) they aren't subtitled. You'll have to wait for them to come out on DVD.
2. Be careful when going to an English-language movie that is animated or has significant scenes in another language. Many animated movies are shown dubbed because children cannot read the subtitles that are usually used to translate English films. Or at some theaters, the one showing will be dubbed, and the next will be shown with subtitles. So you'll have to check on that. When watching movies that may have scenes in another language, those sections may or may not have English subtitles. The alien language spoken in Star Wars was subtitled in both English and Chinese, but Elvish in Lord of the Rings was not. Not a big deal if it's a small part of the movie, but if it's not (like in Proof of Life) you'll be in trouble.