How does a bike absorb all the energy in landing from a big drop? There are countless videos showing BMX/freeride/downhill etc. riders jumping and dropping from heights. For the unprofessional spectator, they seem impossible to survive.
From the physical point of view, the bike reaches the ground with a given kinetic energy which is dependent on the height of the drop and on the combined mass of the rider and the bike. Where is all this energy dissipated? I assume that most of this energy is absorbed in the bike, and some by the rider. How is this energy distributed in various components of the bike?
Physics!
Landing big jumps is all about dissipating the inertia that pesky old gravity has created on your trip back to earth. The better you dissipate that inertia, the better the chance that you wont kill yourself. There are several factors in play here:


The Transition of the Landing.The landing is almost always sloped downwards. Combine forward momentum with a downslope and you've got a significantly softer landing than you would landing on flat ground. That's one of the major reasons you see riders get hurt when they overshoot a landing transition.

Suspension.A little bit of suspension goes a long way, and a lot of suspension goes even further. The amount of impact damping that even an inch of give will provide is enormous. Think about it in terms of what it feels like to fall backwards onto a mattress vs falling backwards into tall grass or snow, distance being equal. The give of the soft surfaces decreases your velocity and dissipates your inertia which is what keeps you from cracking your head open as you would on concrete. Big-hit bikes can have 8 or 10 inches (or more) of suspension travel. That's a lot of travel to dissipate an impact. Even the tires provide a little bit of squish which is especially important for BMX riders (and it's also why rigid mountain bike riders tend to run larger volume tires). 
Proper Landing (how you leverage your bike and the bike's suspension)Notice how most riders will land rear wheel down first, especially on flatter landings which are common in trials and street BMX. This further reduces impact because the rider can, in a way, leverage the give of the front and rear of the bike in succession. This is effective for both rigid and suspended bikes. By landing on the rear wheel first, you can use the bike as a lever of sorts - absorbing part of the impact and decreasing your body's velocity before the front wheel lands. This is achieved if your weight is balanced correctly by bracing against the pedals and handlebars. The effect is even greater for a bike with suspension. As the rear wheel hits, the rear shock soaks up what it can, then the front wheel comes down and the fork soaks up even more. Compare this to landing totally flat (both wheels at the same time) where the bike will provide roughly only as much suspension as the averaged travel of the combination of the front and rear shocks, or for a rigid bike, only as much as the tires would give (ouch!). Landing rear wheel first doesn't mean you get double the travel, but it certainly gives the bike more time to dissipate the force of the landing.
Knees and Elbows (even more suspension)Really, this includes most of your joints - any part of the body that can flex and move to soak up the impact. You don't see riders taking big jumps and landing seated. That's because they're using their arms and legs to take up as much of the impact as they can that the bike couldn't.


When you combine all of these elements in harmony you've got a really substantial amount of movement, and although it only takes a fraction of a second to land a big jump, it's enough time to slow down a rider's mass and keep them from becoming a grease spot at the bottom of The Tooney Drop.