Framing an artwork, as you may have learned already, places more emphasis on your work and gives it a sense of greatness, completeness, realness and importance. It is a good idea for you to keep this effect intact.
If, on the other hand, your artwork is framed is a cheap $5 piece of junk somebody gave you at a White Elephant party, you will want to crop it out just as you would remove other distracting elements from your composition. Then rush to your nearest frame shop and do justice to your creation.
Whether you crop to the edge of the painting or to the edge of the frame, be wary of two potential problems - parallax and viewfinder misrepresentation.
Parallax is the effect of looking through a viewfinder that is distinct from the camera lens itself. Most point & shoots have you look through a small opening that is an inch or two away from the actual lens. As you get closer to you subject, what the lens sees and captures in an image will shift away from what you see. Do you want to know the solution that these camera manufacturers have held to for decades? Shift it back; guess how far off you are and reframe your photo. This usually means forcing yourself, when you compose, to eliminate the edge of your shot that is furthest from your viewfinder. To overcome the psychological resistance we have against cutting off a perfectly good edge is tough; to get it right is even harder.
The other potential problem is caused by viewfinders not showing everything that will appear in the final image. Most viewfinders only show about 90 percent of the actual image. When you try to get real close - so you eliminate any distracting background - you may be surprised by final images that have a wide border of distracting junk around your artwork. The best solution in this case is to know your camera. With my Canon, for example, I would zoom in about a centimeter of a turn to eliminate stuff along the edges.
1) How to Photograph Paintings - Introduction
2) Turn Off Your Flash
3) Up Against the Wall
4) Dealing with Frames
5) Dealing with Glass
6) Digital Fixing