All the time. Small rivers and creeks are my favorite, along with swamps and vlies. Not whitewater rivers above class 1, although I may have done so occasionally in my more expert youth.
In the East, especially the Southeast, there are thousands of sub-class 1 rivers, creeks and spring runs that are called smooth water rivers or brown water rivers or black water rivers. Many of these are so slow that you can paddle them upstream or downstream. Not many of these U.S. rivers can support long, multi-day canoe camping trips as in Canada, but many solo paddlers have done long Canadian rivers.
I have solo paddled many tidal rivers on the east and west coasts also.
Here is a put-in on the Silver River, a first magnitude spring run in Florida:
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