True, and I mention the animation only as historically where this search started for me.
To stay in context with Mark's original question, I think you have to consider what each person's goals are. 

For Mark, and many of us, the goal is to remove the antiseptic sting of a clean 3D render. If the goal is to make a computer painting that looks like an oil painting or watercolor there are many programs and techniques for getting there. And as you mentioned above, not surprisingly, they require painting!  : )

Mark's request was for the technique that doesn't require painting. My response is, those popular photoshop actions often step on your rendered information doing more damage than good. But I'm being general and specifically there are all kinds of post tricks one can do to minimize the 3D curse that don't require turning the whole image into a Rembrandt or Van Gogh. 

And don't get me wrong, doing the latter can be cool too. Like I said it depends on your goal. 

Mine specifically, and how I got interested in this thread, is dealing with sequential story panels and creating a cohesive style that I can apply to 3D images so that I can feel free to paint in other elements and not worry about the two worlds clashing. I do a lot of post already adding effects that are too time consuming to do in 3D. Time is always an issue. And as such I guess I should stop rambling.

It's all very case specific and goal dependent. 

cheers