I'm sure the other post is comprehensive, I haven't read it for its physics/hydrology/chemistry content.
**Puts on his Chemistry/Physics Hat**
All liquids move towards a point of "lowest energy" (i.e. closest to the centre of the relevant planet) by the path with the "least resistance".
Least resistance has two parts: descent rate and the ability for the water to alter its surrounds. Given the options of trying to make a gully in granite or in nice loose black soil... the river will move to the soil and then take the path which maximises the descent and takes the path through the most "movable" material.
Take an example with a big mountain range. The river will move fairly straight through natural cracks in the rocks (opening them up further... see The Grand Canyon) and take very few sharp turns, rarely double up on itself or anything similar without a VERY VERY good reason.
Once it leaves the mountains it entirely depends on the slope to the ocean. If the land is basically flat (barely ANY slope at all) the river will wander all over the place until it finds the path with the most easily moved material.
My advice: Use Google Maps to look at China. Plenty of rivers. They all start in mountainous areas, flow straight for a long-ish period of time and then start straying when they hit the wide flat lands across most of central and coastal China.
Deltas = wierd places where rivers get confused and hedge their bets by splitting and taking as many paths as they can push water through. Nile River Delta, end of the Mississippi river...
Australian Rivers = we have a near monopoly on the concept of a "sand river". There is a river flowing, but it's underneath/through 5m depth of sand and only really flows above-land when you've REALLY got water flowing.
As an explorer, if you ever got lost, the solution to getting to somewhere nice and hospitable was find a river and follow it. Eventually you will hit the coast. Don't try this trick in Australia... it doesn't work quite right and we have the dead 1800s-era explorers to prove it.