Rene Engström - Children Films

Babe! My sister and I just watched it yesterday. It was her first time since she was a kid. Not me, though. Ha! As for the sequel, Pig in the City, I enjoyed that one a lot more. But honestly I think some parts are too disturbing for kids. It's the violence inflicted on animals. I first saw the sequel when I was probably eleven and i didn't watch it again until after I was an adult because it bothered me so much the first time.

Princess Bride
Stardust(the animal sacrifice scenes (just off camera) might be a little too rough, also the fact that the villains want to cut the heart out of one of the main characters, oh and the roast cat on the campfire, but other than that... :3)
Twice Upon a Time (1983 -animated)
Fantasia
Heartbeeps(1981 - being a 30 yr old movie about robots it *is* a little bit dated. I still think it's cute though. So if you see it for cheap...)
Legend(1985)
Nightmare before Christmas
Coraline
Batteries Not Included
Mirrormask
Wallace and Grommet: a Close Shave (animation short)

To be honest, I've always hated "The Last Unicorn" but that's just me. I think it was just because I never liked unicorns. There was a film when I was a kid and it was the dragon version of that movie, something like "the flight of dragons". I watched all the time. If you guys like muppets, they have a whole realm of movies. Then there is "Labyrinth" and "The Dark Crystal". I also was recently shown a movie (which might be hard to find thought you could probably download it or something) "The Halloween Tree" which is a story by Ray Bradbury exploring the history of halloween. If your kids like comics/superheroes, most of the animation done by Bruce Timm, such as batman the animated series and the subsequent movies, are really well done. Also, don't forget about the Pink Panther, with Peter Sellers. Those are amazing, though there may be one movie with a reference of taking a woman to bed. Not super explicit, but you don't want that sort of thing then you may want to wait on some of those movies.

Is The Secret of Nimh somewhere in your collection? The Princess Bride might be a good idea too.

The Iron Giant. Hands down, one of the best movies ever.

The Brave Little Toaster
The 5000 Fingers of Dr T
Yellow Submarine
Felix the Cat the Movie
The Cat From Outer Space
The Computer Wore Tennis Shoes
The Iron Giant
Matilda
Batman (1966)

I must say that while "Real Genius" is a very funny movie, I don't know if it's a "family film." Indeed, compared to the others on the list, it seems a little too mature (or immature in a raunchy sense) ... maybe I'm wrong.

But if you do think it's worthwhile, then I'd add "Weird Science" to your list, too.

You might want to check out some of the live-action Disney movies from the 1970s:

Gus
The Apple Dumpling Gang
Escape from Witch Mountain
The Million Dollar Duck
Freaky Friday
The Shaggy D.A.
The Cat from Outer Space
Pete's Dragon
The Black Hole
and a whole slew of "Herbie the Love Bug" movies

... just to name a few. (They had at least one or two releases every year.)

Honey I Shrunk The Kids is also a good live action possibility from Disney

All I have to say is that Return to Oz is a scary fucking movie!

Summer Wars is REALLY good! And this might be a stupid question, but have you seen the other Ghibli movies? Other than Miazaki. I like My neighbour the Yamadas.
I think the Chipmunk Adventure (1987) is a good movie as well, but it might be too silly for your kids. But if nothing is too silly then I recomend early Toei-movies, Puss in Boots 1-3, Animal Treasure island, but you might have seen them since they are semi Hayaoi Miyazaki.
And yeah by the way, see Pelle Svanslös (1981) and Resan till Melonia.

Also, have you guys seen Watership down?

(Hi! Here via friendsfriends.)

E.T.
Time Bandits

War of the Buttons
The Secret of Roan Inish

Have you seen...
Cloudy With a Chance of Meatballs? or Megamind? I've always loved off-beat humor and I think those are perfect.
Road to El Dorado and Treasure Planet are oft-forgotten but amazing.
The Rescuers Down Under was a favorite of mine growing up (the prequel bored me).
Little Nemo and We're Back! are also good ones that may be a little difficult to find.
Not sure if they'd like A Series of Unfortunate Events, but it's different from most of the children's stuff out there.
Prince of Egypt.
FERNGULLY. Oh, gosh, Ferngully, definitely, if you haven't seen it make it a must.
BALTO, for sure.
SINBAD = awesome.
An American Tail/Feivel Goes West.
Monster House.
A Goofy Movie.
I'll stop now. Hope this gave you some ideas.