Rivers flow downhill--always. They flow downhill from a source toward either another river, a lake or an ocean. That is the simple explanation. However, other determining factors dictate the direction and flow of a river. A few widely-held misconceptions need to be straightened out, as well.
Rivers begin at a source--usually on mountain or a peak--and flow downhill toward the mouth because of the gravitational pull. There are, however, rare instances where rivers will flow uphill temporarily. Nezzete Rydell of the National Weather Service explains it this way: "Where water is forced to move uphill, for short distances over rocks or small inclines, the force of the flowing water must be sufficient to overcome the gravitational pull downward or the water will stop flowing." Needless to say, this rarely occurs.
Rivers always tend toward the path of least resistance. They will wind their way around rocks, trees, buildings and other obstacles searching for the easiest path. Rivers flow this way because it is the most efficient way to move towards the sea. Even over relatively flat land, rivers will often wind and snake to avoid even the smallest obstacle or change in terrain. This is often referred to as "meandering."
Rivers meander in search of lower elevation. Rivers flow in the direct of lowering elevations, not in a straight line from source to mouth.
It's often assumed that all rivers flow southward. And while a majority of rivers do flow southward, there is no physical law dictating it. Perhaps people believe this for same reason they confuse up with north. Or maybe it is because this is the way our maps are oriented. But whatever the cause of this confusion, it is totally false. Many rivers flow north. It isn't a matter of north or south; it's only a matter of downhill.
Many large and famous rivers that flow northward. Perhaps the biggest and best known north-flowing river is the Nile River in Egypt. The Nile is the longest river in the world, measuring over 4,132 miles and crossing through five countries.
Other notable north-flowing rivers are the Niagara and St. John's in the United States, the Ob and Yenisey rivers in Russia and the Magdelena in Colombia.