To fall down x off x out

To fall down 
* I fell down the stairs.
* I fell down and broke my leg.
* He fell down and hurt his knee.

To fall off
* The book was on the table. When the earthquake hit, the book fell off (the table)

To fall out
* His keys were in his pocket. When he was jogging, his keys fell out (of his pocket)

source: Transparent English