Before going much further I need to acknowledge that there are written sources on falls from fight directors far more advanced than myself. By way of example, an excellent technical manual is Combat Mime: A Non-Violent Approach to Stage Violence by J.D. Martinez, is one of the standard texts on unarmed combat and a book I strongly recommend for anyone pursuing any long-term study of physical performance.
Anyway, let's talk a bit about falling on stage or screen. (Like some of my other posts, this is probably an early draft of something that I'll expand into a more in-depth article or paper later on.)
Most importantly, the actor must be able to get to the ground (or bed, or couch, or wherever) safely. There are all manner of techniques to do this, and all manner of things that can go wrong if they "just fall" (concussions, broken wrists, broken tailbones, etc.). They must be able to reliably perform the choreographed fall in a way that is safe for them repeatedly. I'm saying all of these seemingly obvious things early because they are all too often not obvious, and because safety is the first and ongoing concern of any fight director.
Now, assuming that safety is being insured, if a character is falling, there is of course a reason that they are getting to the ground. Those reasons will vary for each actor portraying the character in each production. Acting is (among other things) a visual art. In fight choreography, we tell stories through movement.
One thing that I repeatedly find myself telling younger actors is that the speed at which their body is capable of executing certain techniques may in fact be far faster than is appropriate for the scene. I often use the sport of fencing as an example. As much as I love it personally, it is far too fast and too subtle to be a popular spectator sport. The untrained eye simply cannot follow the action. Likewise, a reasonably fit performer moving as fast as they can may not only be going faster than is safe, but may be denying the audience part of the story they are trying to experience.
Once the technique of falling safely has been assimilated, adding character to the fall can be addressed. There is an exercise in the Stanislavski system of actor training where student actors walk "as if" certain conditions exist and/or they have certain objectives. (A classic example is "walk as if determined to annoy your downstairs neighbors.") In my Spring 2011 Stage Combat Course, I started experimenting with extensive fall "as if" exercises. I spend a lot of time early in the semester on falling drills, and I realized than once the mechanics of the technique were understood, it was not a large leap to start introducing character situations. One of these was coming through a door as if you had been violently expelled from the other side, which lets an audience in on a character's circumstances immediately upon seeing them. Others were isolating a particular body part as if it had been shot and then falling, various states and types of intoxication, fainting, and of course, the imaginary banana peel. Falls could be front, back, just to the knees, rolls (front or back), and/or any combination of these. They could be comic, dramatic, or absurdist, so long as they were safe and had a clear narrative.
I recently put these concepts to use in a rehearsal for a high school production of Almost, Maine, which includes a scene called "They Fall," in which two characters are falling in love, and literally continue falling down throughout the scene. The characters have also been drinking beer all night up until this point. Each admission of affection is followed by a fall. The writing is both comic and touching, but it presents very specific challenges to the performers and choreographer. First, I have to say that I was really gratified to know that this high school understood that they needed to call a specialist in to help with this scene even though it was "just falling," and that I had a great time working with these students. I did not count the amount of falls that are in the scene, but there were many. There needs to be a dramatic build to the ways in which the characters fall and get back up (or partially fall, or partially get up, or fall and roll, or roll to a standing position and then take a spill) that supports the text of the play, keeps the actors safe, and can be consistently repeated every performance.
This was largely a scene where characters were falling on their own. Now think about scenes in which the fall is a continuation of the story of a character being struck (perhaps by a weapon). Someone who was just hit by a baseball bat will fall differently than someone who was shot with a tranquilizer dart, which will again be different from a character who was punched or flipped or kicked (and a kick to the head is a different physical narrative than a kick to the groin). In these cases both the narrative of the successful attack landing and that of its result need to be clear (and SAFE).
How an actor uses set pieces also plays into the narrative of how their character gets to the ground. I recently consulted for a production in which a character was supposed to have a heart attack in a scene during which they had a long monologue. They did not simply fall to the ground, but used set pieces and other actors while simulating various visible symptoms to allow the physical narrative to unfold.
Not going to get into falling down stairs right in this post. Stairs are complicated. Go search YouTube.
If we are dealing specifically with film, there are stories that can be created with editing. Starting a fall, stopping the action, and then cutting to them "completing" the fall with the actor already on the ground/in a pit/at the base of the skyscraper is a safe and effective way to tell a story without having to film the fall itself (unless you are working with Jackie Chan, in which case you have my envy).
Falls are often a key part of physical narratives. They need to be studied so that they are safe and dramatically effective. They're too often overlooked, and they're an area where actors have great opportunity to make powerful comedic or dramatic choices.
Work on them.