If it looks like my kind of thing, I’ll go see it. Actors, writers, directors etc mean very little when it comes to picking and choosing. I barely pay attention. Occasionally I won’t see something because of some actor I find irritating or talentless, but not the inverse.
However, of your options, I chose “franchise” because that can be a strong factor, but “genre” is a closer match.
Early 40s.
I think we already had this discussion, but whatever. I’d read the Hobbit as a lad and was pleased but not enraptured. We didn’t have a lot of money growing up, so most of my reading was done from the library. The local library only had TWO TOWERS–in an edition not even having the “What has gone before…” bit–so can imagine why I abandoned it after about two pages. More importantly they had THE MOON IS A HARSH MISTRESS, so I got distracted by the admiral.
Jump ahead twenty years. I got dragged to FELLOWSHIP and loved it; read the book from the beginning and loved it more; then read SILMARILLION and loved it most of all.
This is basically my answer (even the part about Tarantino and the Coens), except that I will see pretty much any movie with John Turturro in it.
I’ll only pay to see a movie in the theater if it seems like the movie needs a big screen or a big sound system to be fully experienced. Avatar is a good example, also Coraline 3D.
Pretty much the same for me. I enjoy…and prefer…watching things on my own time, at home, so to get me to a theater willingly the film has to offer something I can’t get at home. And I’m not talking about the popcorn. 
Among things you listed, director and screenwriter are about tied for me.
I only go see films in Cinemas if I know it is going to be a spectacle, a visually impressive, action filled epic that really needs to be seen on a massive screen with surround sound. Thoughtful yet stirring drama? That will be just as stirring on my home TV thank you very much, with the bonus of no assholes making any noise.
But the blockbusters? They need to be seen on the big screen. For example, I never got to see Saving Private Ryan at a cinema, something I regret for obvious reasons.
So, actors, directors, source material, etc, etc. None of that matters.
If the movie or subject is something I’m interested in, or I like the work it was adopted from, that would be my first consideration. Then the director, then the actors (if one of my favorite actors is in a supporting role that’s good enough).
I’m rather surprised that you left out the genre. If it is scifi or a war movie, I’ll go see it unless it gets really bad reviews. Most comedies can rot in hell for all I care on the other hand.
Voted for the franchise, but really it depends on what kind of movie it is (action or sci fi YES, horror or comedy MAYBE, chickflick or romcom NO), and how it looks in commercials. For instance, all the hype and commercials for Avatar really worked against it for me, as I just didn’t think the CGI looked as great as everyone said it did, so I didn’t see the movie, even though it fits the supposed YES categories for me.
I have gone to movies based on the lead actor (I think I went to everything Ahnold was in post-T2) or lead actress (like anyone went to see Barb Wire other than to ogle Pam Anderson) but can’t say that I’d ever go see a movie just based on director/writer, unless it’s a franchise the director/writer is particularly tied to (Joss Whedon and Firefly/Serenity for instance). Supporting actors, I don’t think they’d influence me too much.
Adapted from a book I liked (LotR, Narnia) or TV show (whether a continuation like Star Trek or Serenity or reimagining like Star Trek or Mission Impossible) sure, unless it looks like utter crap in previews, I’ll be very likely to see it. Video games… well, I have done it, but track record makes it much less likely in the future.
I’ve never liked the Daredevil character or comics, but I thought the movie was pretty good. Much better than I expected. This is the original version, not the new cut released on DVD a few years later that everyone seemed to think made it a better movie (haven’t seen that version).
I put down adapted from novel, but the real answer is that the premise or genre are the biggest factors for me. There are some directors/creators (Nolan, Whedon) and actors (Gordon-Levitt, Glau) who will draw me in too, but premise and genre are far more often the prevailing factors. Occasionally certain people (Cruise, Allen) will make me shy away from movies.
I’m more likely to see a summer blockbuster in the theatre because special effects and sound are likely to be more important. A dialog driven movie can be seen on my home system just as well as the theatre. A special effects driven movie? Not as much.
But most of all a good director utilizes a good DP effectively, and that’s really the only reason to pay so much to see it on a big screen.
I’m likely to go and see a movie at the theatre based on a combination of “Interesting Trailer”, “Appealing Story”, “Actors/Actresses In Said Film” and “Director”, with a few exceptions for things like “James Bond Movies” which I’m going to see anyway regardless.
I’m another who’s surprised that genre was left out. Or plot, for that matter. I think plot has the most influence on whether or not I see a movie–I’m not interested, for example, in romances or juvenile comedies.
I picked “a tie between two or more,” the two or more in mind being franchise (for example, I’ll watch any and all Harry Potter movies, 'cuz, well, you just gotta finish the story!), actor/actress, and director. It depends, really. I like Christian Bale plenty, but he wasn’t enough to make me want to see Terminator Salvation, because I have no interest in the Terminator franchise.
I did, however, see The Prestige based solely on the fact that Christian Bale and Hugh Jackman were in it. Of course, this was also because my friends wouldn’t tell me what it was about, so all I knew about it was the fact that those two were in it. Not that that hurt its chances, of course :D. There are also actors I try to avoid, namely Nicholas Cage (though I will concede that he was good in Kickass).
Reviews are also important–not just professional reviews, but those of my friends as well (if our tastes match). I tend to agree with critics much of the time.
I go with what some others have already said. The reasons listed are all reasons why I might watch a movie in general. But the most likely reason why I’d specifically choose to see a movie in a theatre is because I feel it has visual effects that are best appreciated on a big screen.
I choose the last option because what makes me want to see a movie is if I think the plot looks good. It doesn’t matter who is directing, starring, writing, etc. if I hear/see something about it and think “That sounds like it will be interesting. I’d like to see that.”
Mostly I only consider seeing a movie in a theater after I’ve eliminated them by a lot of variables. There are a lot of actors/actresses that I avoid, for instance. I don’t like most horror, especially not the gorier sort of horror. I don’t like most feel-good movies, or vehicle movies. I won’t see a movie that seems to have great special effects as its main draw. And I’m not likely to go watch a kid’s movie in a theater, even though I generally enjoy kid’s movies, because there are likely to be a lot of kids in the theater (what a surprise!) and I don’t like people of any age running around and screaming. Also, the kids are more likely to be dropped off at the movies while the adults go do something else.
Three are tied: actor, actress and director. It varies from movie to movie, but it’s sometimes combos of two of the three, and sometimes all three.