I really like all the recent posts here.
My own (very loose) definition of an abstract is something like this: "Any image that is interesting or fun to look at, where the interest doesn't lie in what the 'subject' was but rather in the visual effect produced."
In one sense, every "straight" photo is abstracted (via cropping in camera) from the scene in front of the camera, so I don't bother with that formal definition.
But that may be just me.