Seems like most end up in either of those categories.
For most men’s stories, dramas and comedies as well as action movies, the women are extras or props to be rescued.
Or else all the stars on the posters are women and the men are backgroud stereotypes, either mean or weak.
Of course the date movie boy-meets-girl love stories are fairly balanced.
What dramas or comedies have balanced casts?
**Alien
Aliens
Mary Queen of Scots
**
The Big Chill
Woody Allen movies
Nora Ephron movies
Garry Marshall movies
Eraserhead.
Nora Ephron? She’s the Jerry bruckheimer of Chick Flicks
I’m pretty sure that if you say her name three times while looking in a mirror, she appears and lops your nuts off.
Nora Ephron movies are definitely chick flicks.
I’m going to have to nominate three of my favorite movies:
Apollo 13
Almost Famous
A Beautiful Mind
Ocean’s 11 (the remake)
The 40-Year-Old Virgin is a “neutral” flick.
That is, is has two story lines proceeding along simultaneously, one with guy themes and one for the chicks.
Thank Og no one else is still in the office.
I’d say any Pixar animated feature goes for mass gender-neutral appeal.
Manos: The Hands Of Fate is unsuitable for human viewing, regardless of race, sex, religion, physical handicap*, et cetera.
*Well, I suppose it might be OK for someone who is blind and deaf.
This may only apply to English (and probably Theater) majors, but I think Shakespeare in Love is gender-neutral, if barely. 
Oh Brother, Where Art Thou?
I always thought Roadhouse. The guys dig the fights, and the monster truck scene. The chicks have Patrick Swaze to stare at for the entire film.
YMMV
Sgt Schwartz
The Red Balloon.
Titanic had weepy doomed romance for the ladies and a ship hitting an iceberg for the gents.
Serious socially relevent movies, like Schindler’s List and Saving Private Ryan.
Out of Sight? I haven’t heard any men specifically say they like it, but I think it hits both categories in the “guy movie” vs. “chick movie” debate. Guns, crime, and prison fights for the guys, George Clooney and Jennifer Lopez doing the “love from the wrong side of the tracks” thing for the girls.
Plus, I don’t care who you are, that trunk scene is just hot.
Just a few picked from my own collection:
The Hudsucker Proxy
Casablanca
Brazil
Being John Malkovich
Topper
Serenity (which every man, woman and child ought see, several times, and buy DVD copies of for all their friends :D)
Call me wacky, but I think most flicks are more or less gender neutral. ‘Guy’ flicks tend to be your more action oriented fare, although sometimes with deeper masculine stuff going on (Lawrence of Arabia comes to mind). ‘Chick’ flicks tend to be… about… uh, girly stuff, you know? All sappy and such. (Does it show that I don’t watch many of these, heh?) Most movies fall somewhere in the middle. Maybe it’s just my particular taste in film, though.