What is the scale of the map (that is, how big are some of the prominent features)? The amount of land area visible will have a big impact on the number and size of rivers that you have.

Also, you have a lot of mountains, suggesting that this map covers a large area. The more mountain ranges between the sea and a land area, the less rainfall will make it to the area; this lack of rainfall usually translates to a reduced number of rivers in an area.

http://www.cartographersguild.com/tu...ght-place.html is the popular discussion area for this topic. Try reading through that and see if it makes sense.

There is really only one rule for rivers, though: water flow downhill until it evaporates, until it sinks into the ground, or until it pools into a pond, lake, or sea. Everything else is derived from that one rule (and the context in which the water is doing the flowing, of course).