A river profile with a steep drop can indicate the presence of a fault or a resistant rock type.

Image sources:
http://epod.usra.edu/archive/images/wallace_creek_aerial.jpg

In areas of active deformation, the surface of the earth is deformed by faulting and folding. Offsets or sudden changes in the gradients of rivers are useful indicators of recent tectonic activity. These types of studies can help identify a trenching site for a paleoseismology study.

Winding, meandering rivers can indicate a very shallow slope or a slow rate of uplift.

Very straight rivers can indicate a steep slope or a high rate of uplift.