Antagonists and protagonists should be so for good reason. Movies where a lover who tears apart a marriage is also portrayed as the protagonist should be avoided for example. Movies where you find yourself rooting for the thief to succeed perhaps.
Implicit in this first criteria is that it's okay to watch people portrayed doing wrong things. If adultry takes place, the film should help us see how hurtful it is though. If someone is portrayed as being a great parent then the film should portrary them as admirable. Violence should not be glorified. Divorce should not be played over lightly.
Practically-speaking, never watch a movie with your kids (or allow them to get see a movie) that you haven't first looked up on iMDB.com's parental guide or on pluggedin.com. I would even recommend doing so for movies you've seen before. Sometimes we see movies through a different lens once we have kids.
One thing about this mutual acceptance of a family movie is that all family members need not enjoy the family movie on the same level. When I watched Hugo with my kids a few weeks ago, we all loved it but they didn't get some of the undertones in the movie (the motif of purpose and brokeness). They were able to see that when we discussed the movie afterwards but they would have enjoyed the movie all the same had they not realized that the movie wasn't so much about fixing man-made machines as it was about fixing the lives of those men.
I have enjoyed exposing my kids to many good films and by doing so have expanded their horizons. They got a glimpse of what it was like to grow up in communist China in Mao's Last Dancer. They'll see racism when we watch To Kill a Mockingbird or Look Who's Coming for Dinner. Right before they leave our home and go off to college, I want to watch Citizen Kane with them so they'll be forced to graple with what's really important in life (and what's not). I want them to see Gattaca with me so we can discuss how no one should limit their potential.
Not every film has to have this heavy of a moral. Not everything has to be historical or even serious. But there ought to be room for a conversation. Questions like, "Why do you think the film maker choose to do this?" or "What was the funniest part to you?" will do fine.
Here is a very random list of films I consider to be "Family Movies" for an age-appropriate family of course, and as always look up the parental guide on iMDB.com before watching any family movie with your kids, even if you've seen it before:
Citizen Kane
To Kill a Mockingbird
The Prestige (warning: PG-13)
The Sting I & IIThe Great Escape
The Sixth Sense (warning: PG-13)
The Bourne Trilogy (warning: PG-13)
Star Trek (the JJ Abrams one; warning: PG-13)
Gandhi
The Princess Bride
Big Fish (warning: PG-13)
Pirates of the Caribbean (warning: PG-13)
Patton
The Truman Show
Mutiny on the Bounty
Guess Who's Coming to Dinner
Gattaca (warning: PG-13)
Back to the Future
Ghostbusters
Paycheck (warning: PG-13)
Better Off Dead
Minority Report (warning: PG-13)
The Goonies
Clue
Patch Adams (warning: PG-13)
Seven Years in Tibet (warning: PG-13)
Jumper (warning: PG-13)
The Hunt For Red October
Salt (warning: PG-13)
National Treasure
August Rush
Mao's Last Dancer
Babies
Apollo 13
Hugo