When installing drywall, as shown in Figure 1, around windows and doors it is important that the position of joints between sheets of drywall be towards the middle of the opening rather than at the corners.
Figure 1 - Drywall panels
For most home handymen it would appear that when installing or hanging drywall that the most convenient method of installing the drywall around window and door openings would be to cut and install the drywall sheets to the vertical edge of the opening, as shown in Figure 2.
Figure 2 - Incorrect drywall joint position
Note: The drywall joints are shown in deep blue.
However, although this may be the easiest method of installing the drywall sheets and will most likely have the least amount of waste, in the long run it is a recipe for cracking.
When buildings settle, and all buildings will settle to some degree, the vast majority of the stresses are placed in the corners of openings. This means that if the drywall joint is located in the corner of the opening it is more likely to crack at that point.
Secondarily the finishing of the drywall joint at the corner may make installing window or door trim more difficult.
The proper method of positioning the sheets of drywall around windows and doors is shown in Figure 3. The drywall joints are shown in deep blue.
Figure 3 - Correct drywall joint position
As you can see in Figure 3, the edges of the sheets of drywall wrap around window and door openings rather than the edges butting up against the edges of the window and door openings.
Professional drywall installers will often hang the drywall over window and door opening and then using a drywall saw or high speed rotary tool cut the opening out of the drywall.
Additional information on drywall installation.
Additional information on hanging drywall on curved walls.