Without a scale, it's hard to say how realistic the rivers really are. My first instinct is that they are a little wiggly if this is a continental-scale map.

Overall, though, the river systems look plausible. They generally start in the highlands (with a few exceptions like the one in the lower-left corner of the map where a river starts near the sea and flows between two mountain ranges on its way to another sea) and end in the sea. There do seem to be a lot of rivers, but that may be a scale issue.