Not very rigorously defined, but here's what http://geography.unk.edu/corps/lessondraft/class2.html
had to say...

Brook – a natural stream of running water smaller than a river or a creek.
Creek – a natural stream of running water larger than a brook and smaller than a river.
River – a large stream of water of natural origin, which drains an area of land and flows into another river of body of water.
Stream – a flow of moving water usually of natural origin.