The Version You Know
Well, you've all seen the movie, you know how this goes. Evil step-mom hates that her daughter is prettier than her so she tells one of her men to take out to the woods and kill her, and bring back her heart as proof. He can't follow through, so he tells her to run away and never return.
Snow White flees, and she falls in with seven friendly dwarves. The step-mom finds out and sneaks her a poison apple. Snow goes into a coma until a handsome prince rescues her and they live happily ever after.
What Got Changed
In the Disney film the wicked step-mother winds up dead (she falls off a cliff). So that's pretty hardcore we guess. It's got nothing on the Grimm version, though, where the step-mother is tortured by being forced to wear red-hot iron shoes, and made to dance until she falls down dead (you can picture the puppet thing from Saw spelling this out for her over a closed-circuit monitor).
The issue of Snow's actual age is a point of contention as well. The Grimm's explicitly refer to her as being seven years old when the story starts, and while there's no firm indication of how much time has passed, it's no more than a couple of years. So unless that's an eight-year-old Prince Charming who comes along and rescues Snow, we're backing away from this one before we become the subject of an NBC reality show.
The biggest change, and the bloodiest, is step-mom's ... unusual eating habits. Namely, when she asks her man to bring back the heart of Snow White, she isn't just after proof the girl is dead. She wants to eat it. Depending on the version of the story, the Queen asks for Snow's liver, lungs, intestines and pretty much every other major internal organ, up to and including one gruesome version where she asks for a bottle of Snow's blood stoppered with her toe.
And if you think the fairy tales were gruesome back then, you should have seen the merchandising tie-ins.