Ulysees said:
Thank you robphy. Have you put them in order of capability?
It's in the order that I thought of them.
They have different strengths... and may or may not be useful for your particular problem, which you haven't clearly specified.
NeatImage is for digital camera noise reduction.
paint.net, gimp are photoshop-like image processing programs
imagemagick is a command-line image processing program
paint.net, gimp, imagemagick support plugins and scripts that can help do intricate operations and automate the process
I'll add in ImageJ, which is useful for [say] medical image processing. There are lots of scripts for ImageJ.
There are free vectorizers like autotrace.
Everything listed is free (although NeatImage's free mode has some limitations).
...but as it's been said... it really depends on what you need it to do.