* They always flow downhill, never uphill
* They take the path of least resistance. "Resistance" means how much erosion the flowing water would need to cause in order to shape a path through the terrain: A river will find it much easier to run along the center of a valley than to plow through the surrounding hills. On flat terrain the river is more likely to head where the soil is softer.
* Rivers start narrow on the highlands, and become wider as they reach lowlands and head toward the coast. Rivers crossing relatively flat terrain tend to meander (doing zig-zag turns).
* Rivers almost never split - tributaries flow into the main course, not out of it. The major exception to this are deltas, where big rivers reach the sea.