The county provides a watershed map (here) which shows the drainage basins for the major rivers in the county. These rivers are the Huron, Raisin, Rouge, Stony Creek, and the Grand. Below is the inset map from that page.
Recalling the surficial (quaternary) geology map from MDEQ’s GeoWebFace (below), we can see how much what happened during the Ice Age still affects us.
The Huron and Raisin still follow the old paths of their ancestral rivers (shown in pink as “outwash sands and gravels”. The Huron through Dexter to Ann Arbor and then Ypsi and the River Raisin south from Manchester down to Clinton and then south out of the County. Fleming Creek (a tributary of the Huron) also (more or less) follows the pink lobe going Northeast into Plymouth Township. At some point there was also a river that connected what now is Saline and Clinton that no longer exists.
Although not as discernible on the geologic map, I think it’s really cool that there is some watershed for the Grand River in the county as well – all that water is going west to Grand Haven with everything else in the county going east to Lake Erie or the Detroit River.
The blue and white represents lake sediments placed in glacial Lake Erie (aka Lake Maumee). As this lake receded, the rivers that discharged into it continued to extend into areas that were once lake in order to meet it. The Huron kept chasing it south-southeast, the Saline River was formed heading down to Milan and out of the former lake, the Rouge, Stony Creek and Swan River watersheds were also formed.