I usually scan with a fairly flat setting -- I try to get all the basic levels right in the scanner software, but I am wary of clipping at either end so I go for a fairly conservative scan.
After that I usually do some sharpening and some level/contrast adjustment. I very rarely do anything else. I may rotate the photo slightly if it's off vertical: I have an annoying habit of leaning fractionally to the right, so photos often need a 1-degree counter-clockwise rotation.
I do sometime do noise-reduction on very grainy film scans. I never do dodging and burning, any contrast/level adjustments are global and usually fairly small.
That tends to be it. I bought a copy of Silverfast recently, and I find it gets the levels close enough that increasingly the only post-processing I do is sharpening appropriate to whatever print or screen size I want to use.
I'm not against substantial post-processing in principle, I just don't find it works for me personally.