The player does not take fall damage if they fall on the edge of a block.

If a player jumps (For example) of a cliff and hits the corner or edge of a block the player landed on, he will not take fall damage. The part of the block that the player falls on to has to not be connected by another block (For example if you fall in between two connected dirt blocks it will not work.).

(This probably works on a lot if not most of the versions.)