A cabinet door can become stuck either because of a hinge problem or because the cabinet door is obstructed by something inside of it. There are several ways of getting the door open when this occurs.
Opening a Stuck Cabinet Door
The first step in getting a stuck cabinet door open is to determine what is causing the door to stick. If the hinge is locked and preventing the door from opening, try spraying WD-40 or another type of lubricant on it.
Sometimes an object in the cabinet can become lodged in the door or the hinge and block it from opening. If that happens, you may be able to open a cabinet next to the stuck door and reach inside to dislodge the obstruction.
If the cabinets are made of wood, it is possible the wood of the door has expanded against the frame of the cabinet due to a change in temperature. This is more likely in the summer.
If the door is wedged into the frame, try using a straight object as a lever to pry open the cabinet door. A flat-headed screwdriver is ideal for this. By wedging the tip of the flat head into the seam between the door and the frame (on the side opposite the hinges) and then pulling the screwdriver out perpendicular to the frame, the door should become unwedged. Be careful when using this technique because it could scratch or damage the door and the frame of the cabinet. Also be careful not to cut yourself on the screwdriver if it slips out of the seam.
Another option is to remove the hinges from the cabinet using a screwdriver and, once the hinges are off, pull the door off the frame. This is an extreme method that should only be used as a last resort unless you plan on replacing the cabinets anyway. Once you get the door open and are sure of what caused it to stick, try to make sure the situation is resolved before closing the cabinet door again to make sure it doesn't become stuck again under the same circumstances.