Fall damage, also known as aie or ouch, is a setting where you die whenever force is put on your mouse (e.g. objects hitting you, you falling from high place etc.). It can be added to maps using map XML editing. It can also be enabled in a room through the room creation window added in V1.629.
Mice die when they fall from too high. A ground's restitution value determines the safe drop height (SDH). For normal wood, ice, chocolate, and grass grounds, this SDH is 85px. So if your drop height is 85px, you are safe. If your drop height is 86px or above, you will die. The SDH for trampoline ground is 26px.
Mice die when they are hit by a dynamic object with enough force. According to F=m*a (force equals mass times acceleration), the force depends on an object's mass as well as its movement. This means that an anvil is more likely to cause death than a small box. However, a small box at high speed can be just as deadly as an anvil at a lower speed.
When you fall down, jump right before you hit the ground. Jumping right before you hit the ground resets your drop height to the vertex of the jump.
Landing on a slope is safer. Landing on a slope transfers your downwards momentum to your sidewards momentum. This means that the momentum at which you hit the ground decreases so you can land more safely.
Avoid narrow spaces
Narrow spaces are dangerous. If you see a narrow space, be careful if you have to pass it. Avoid jumping as this increases your chance of dying,
Avoid sliding down slopes
Running down a slope gives you downwards momentum. If you hit the ground too fast, you will die. Avoid this by turning around to slow down before you hit the ground.