The most commonly used answer to the riddle "what runs but cannot walk?" is a river. When water is flowing through a river, it is said that the river is "running," but of course a river cannot walk.
The full version of this riddle is usually some sort of variation of "what runs but never walks, often murmurs but never talks, has a bed but never sleeps, and has a mouth but never eats?" The answer is, of course, a river. A river runs, makes a murmuring sound, has a river bed and has a mouth which is more commonly referred to as a source.