General:
* Stream
* Brook
* Run
* Rivulet
* Gulch (especially in the western US)
More specific:
* Rill (a very small stream)
* Torrent (a fast-flowing stream)
* Burn (Scottish and Northern English for a small stream)
* Gully (a channel worn by water)
* Ditch (a man-made channel)
* Bayou (a slow-moving, swampy stream, often in the southern US)
The best synonym will depend on the specific meaning you want to convey.