(Sorry if this has been covered sufficiently above, not all of which I've read. I saw a "required pocketing accuracy" comment, and had a thought about a simple explanation of the issue.)
The center of the object ball needs to go through a "window" that is roughly the width of the pocket minus the width of a ball. That window is roughly one ball wide. Any more to the left or right and the object ball will at least touch a cushion and will probably miss. On worn cloth you can actually see the width of this window in corner pockets as the rail groove is visible where it goes around the corners to the facings.
I would like to put the object ball in the middle half of the window so that there is a little margin to either side, just in case there is a little unexpected roll or skid. That is, I want my pocketing skills to be accurate enough to "hit the middle half." On most corner pockets, that additionally restricted window is close to an inch wide.
Here is a simple rule of thumb to know how many degrees wide that pocket window is: If the object ball is one cue length away from the pocket, the window is one degree wide. If the object ball is half as far from the pocket, the window is two degrees wide. A full-table-length shot, which is about two cue lengths long, has a window only half a degree wide.
(This is based on another rule of thumb: for a typical cue, the width of the butt plate as seen from the tip is close to one degree wide. In a cue length, a 1-inch width is almost exactly one degree.)
If you prefer to think about the full-width window, just multiply my conservative window numbers by two.
Thanks, Bob. That was much more concise that what GMT has written. I always estimate my targets with the edges of the ball, so that would account for the discrepancies in the discussion.