The biggest mistake most new cartographers make is the rivers do not split as they go downstream. I made the same mistake in my earlier maps (and still do every once in a while).
Rivers generally start at higher elevations (hills, mountains, etc.) and follow the path of least resistance as they head toward lakes and/or oceans. Smaller rivers will converge into larger ones (think of a tree). Another thing to remember is that multiple rivers may feed into a lake, but generally only 1 will act as an 'exit'.
Of course if you have various reasons as to why you don't want to follow these guidelines, then by all means ignore them.