Technically this wasn't IN the movie but the movie inspired it, so it kinda counts.
A schoolboy saved the lives of a schoolbus full of other kids, when the driver had a heart attack, he climbed on to the driver's lap, jumped on the brake pedal and pulling the bus to the side of the road. When asked why he did it, he told everyone that he had seen "that bus movie". That boy is a real hero.
Just before the bus jump, all the passengers are clearly terrified that they are about to die. But then, the bus somehow makes the jump, and of course, the passengers immediately cheer, grateful to be alive. It was nice to see a few smiles in this horrific situation.
As the passengers evacuate the bus, Ortiz yells some words of encouragement to the wimpy passenger who he's been bickering with throughout the movie, "Come on buddy, I got you! Come on!"
And when the poor guy nearly falls off, Ortiz pulls him to safety and gives him a bro hug.
Jack and Annie bonding throughout the film, but especially after they get off the bus and crash the train. Special mention goes to the scene where Jack realizes he doesn't have the key to the handcuffs and desperately tries to get her out of them to no avail, topped off by Annie telling Jack to save himself. Thank God it's a happy ending because it was a borderline Tear Jerker.
The very fact that this film has an exceptionally low body count for an Action film of The Nineties is a Heartwarming Moment in and of itself. Jack and Harry are able to save everyone on board the elevator. Jack and Annie, with a lot of help from his fellow cops and even a little help from the news media, are able to save all but one person on board the bus. In all, only 7 characters died. The building security gaurd, Bob, Helen, Harry, Robin, the subway driver, and Howard. This is probably about as close to an Everybody Lives in an R-rated Action film as you're likely to get. And it's still regarded as one of the best Action films out there, proving you don't need a high body count to make an Action film good.