I agree with sebbbi on the theory that the images should be clean, however the practice is a little bit different.
One thing is that CG, both offline and especially realtime, is just not good enough to look realistic on its own, in its raw form. Obviously the realtime renderers are suffering a lot on image quality, all kinds of aliasing and such, and also the geometrical complexity is not enough either, even for simple scenes and simple objects. Offline is better in many things, but it's still too perfect and artificial looking. The various kinds of lens effects and other post work can help a lot here to hide these issues and add subtle imperfections that help to sell the results.
The Order is probably the best example of this, even if the effects are used a bit excessively.
Which brings me to my other point, which is stylization. Even in photography, many artists chose to abandon realism intentionally, to add their own artistic touch. Things like black and white, using certain types of lenses or film stock, filters on the camera and so on are pretty common and a perfectly valid approach. Or there's studio lighting, smoke and wind machines, or even artificial lighting and other trickery when shooting outdoors. We shouldn't ask CGI to avoid using such tools either.
And then of course a lot of photographers also do heavy retouching, particularly with female subjects, but also with things like food. Yeah it's usually used to excess and I don't like that, but that's also more of a question of style.
So in the end, I believe that anything goes - although preferably with good taste
Certain games would benefit from as little post work as possible, while others would look better with all the tools in the box - it's not something that should be set in stone IMHO.