People often use "realistic" in a very loose manner.  I think there has to be a word that would better describe what people are often trying to describe.

I prefer images that don't call attention to how they were made, but they don't necessarily need to pass for photos either...  I especially abhor aliasing, clothing poke-through, hair intersecting bodies, objects appearing to float due to lack of ground shadows or occlusion...

There was a lot of discussion in a CGTalk thread about the "realism" of a recent Unreal Engine 4 teaser video.  The problem I had with the discussion was that the trailer took place in a fantasy setting and had a lot of "magical" type effects.  I couldn't help thinking that no level of quality would convince me I was seeing something real, and that the makers of game engines would be better served recreating everyday scenes if they want to convince people of the fidelty their engines can achieve.

I worked with scale models for several years, and I think I rather like the plasticky look I sometimes get with SSS.  It's not accurate, but it fools my eye into thinking I am looking at something physical, rather than virtual.  I remember showing a friend a very simple render I did many, many years ago and he gave me the compliment that it looked like a thing that might actually exist.  This was a render done on an Amiga, but it had nice lighting with at least one shadow light, some textures, and just enough geometry that it looked better than the 3D games of that era.  From then on, my goal was to make sure that every render I did seemed to convey a believeable sense of space and solidity of objects (I use depth of field/fogging a lot), even if the resultant image appears to be of miniatures or mannequins.  I also worry a little bit about falling into the "uncanny valley", so I've never really focused on images that might actually pass for reality.   

There just has to be an alarm in the mind that goes off when something just looks wrong, and it probably relates a lot to the uncanny valley idea.  Paintings and other depictions of the fantastic don't seem to set off that alarm, and I try to be careful my renders don't either.