Agree with others on the ratings issue, the '12' in 12A still means 12 - it's just saying that the BBFC think it's generally OK for kids over 12, but if you've got under 12s then it might be OK for them (depending on your individual kids) but it's important that you as a parent make an informed decision, ie ideally watch it first. We have watched some 12As but we always see them on DVD so we can see them first (I'm not paying for cinema tickets twice!).
I agree that all kids are different, and should be free to enjoy an eclectic range of films, but I'm still surprised by some of the films mentioned here for young kids. It's not just about whether a film is 'fine' for kids (ie won't damage or terrify them), it's surely also about whether they actually enjoy it. I think the comment by a PP that 'there's only so much Disney you can take' is quite telling - at this age it's surely a question of what your kids enjoy, not what you enjoy? Yes, it's more fun to watch a good film with your kids than a bad film, and it's brilliant once they're old enough to watch really good films with you, but maybe the watching things too early issue comes from trying to find genuinely adult-pleasing films to watch at this age, rather than sticking to kids' films?
And I just don't get the fast forwarding through the inappropriate bits. If you have to do that, surely it's generally an indication that the film is too old? I want my kids to learn to really love and understand films, and I'd find it frustrating myself to watch a film where I wasn't allowed to see bits of it, particularly as they're often bits that are quite key to the whole film, conceptually if not narratively. The classic one is Bambi's mother getting shot - it's upsetting, but it's essential to the heart of the film, as it gets you to understand the fragility of a deer's life and Bambi's transition into adulthood. If your child's not ready for that then don't watch Bambi! There are loads of other examples here though. The bit at the end of SW3 (even though it's rubbish and the film is shite) is the whole culmination of the story arc. (Actually the bit with Anakin's dying mother and the murder of the tusken raiders is grim but important too, I'd forgotten that bit.) In Twilight, the themes are really adult - it's all about virginity and sexual restraint, not just running really fast up trees, so the sex scenes are really key when they finally happen. The various scary bits in Harry Potter are the bits that let you understand the really evil nature of what Harry is up against, which gives the stories their weight and makes them not just about learning fun spells and playing quidditch.
I'm quite surprised by people mentioning the Princess Bride, too - it's a great film, but very dialogue-heavy. There are quite long stretches which are nothing but quite fast-paced funny dialogue. We did watch it with my kids but my 8 year old drove me mad with questions because he didn't really understand a lot of what was being said, and why some of the jokes were funny. My 11 year old loved it and got most of it, but I'm sure there were still some things that went over his head. I'm surprised younger children aren't bored/frustrated by it.