Fall Damage is suffered when The Spelunker stays in the air for a specific amount of time. He is then stunned for a length of time and may take further damage from Traps or Enemies, making long falls one of the more dangerous hazards in Spelunky.
On normal falls, a fall of eight or more tiles will deal one point of damage, a fall of eighteen or more tiles will deal the Spelunker two damage, and a fall of twenty-eight or more tiles will cause instant death regardless of the Spelunker's current health.
It's important to keep in mind that fall damage is time dependent, standing on a tree branch and pressing down + jump will make the spelunker go through the tree branch at a higher initial speed, which will allow the spelunker to fall a total of 11 blocks without taking fall damage.
Fall damage does not occur if the Spelunker lands in water or has his fall otherwise interrupted, for example by landing on an enemy or by proper use of the Jetpack, Cape or Climbing Gloves to reset your fall distance and speed. Additionally, the damage dealt to an enemy when stomping them after 18 blocks also increases, potentially dealing instant-death to enemies with 10 health with just one stomp. Fall damage might not be taken if the player falls with a Ball and Chain. If the player falls while stunned, no damage will be taken, making it possible for players to stun themselves with a camera or other method to fall long distance in a "safe" manner.
As a quick rule of thumb, if the Spelunker is on the center of the screen and the target platform can be seen without looking down, it is safe to drop onto. Firing a weapon in mid-air however makes the game increase the distance fallen variable.
One particular danger when taking fall damage, is that you can continue bouncing forward with the same horizontal velocity you had when you hit the ground, greatly increasing the chance of the players unconscious body falling into even greater danger.