The riddle
What Runs but Never Walks?
Run as in flow
Run has dozens of meanings, and one of them is to flow. Water runs downhill, a tap runs, and a river runs to the sea. The riddle asks for something that does this without ever walking, which rules out people and animals and points to moving water. Water itself and a faucet are also given as answers, and both fit, though a river is the one most tellers expect.
The longer version
A popular longer form keeps the same answer: "What runs but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?" A river has a mouth where it empties into a larger body of water, a head where it begins and a bed, the channel it flows along. Each clue borrows a body word and uses it for a feature of the landscape. A river also has banks on both sides, which keep the water in its channel.
What pulls it along
Gravity moves river water from higher ground to lower ground, which is why rivers keep running. A river with no slope at all would stop and become a pond. The USGS Water Science School explains the whole path of water, from rain to river to sea.
Water in other riddles
For another riddle that hides a plain answer behind a plain verb, try what comes down but never goes up.