As a house settles, doorknob latches and strike plates sometimes become misaligned, so doors won't latch shut. Usually you have to push the door in, and either pull up or press down on the doorknob in order to get the latch to catch in the strike plate.
If the movement has been slight, there's a very simple fix for the problem. Instead of moving the strike plate, simply slightly enlarge the latch opening in the strike plate as shown above. A rotary tool does this quickly and easily. Use a carbide-cutting bit specifically designed for metal cutting.
Judge the part of the strike plate that needs grinding by testing when the latch catches. If you have to push down on the doorknob, then the top of the strike plate hole needs grinding. If the door has to be pushed in, then grind the outside edge of the strike plate hole.
You don't want the latch slopping around inside a huge opening, so don't grind away half the strike plate. Remove small amounts of metal and then test the door. Repeat until the door latch effortlessly catches the strike plate.
Grinding metal can throw sparks and fragments into the air, so wear safety glasses with side shields, or full goggles when grinding. Otherwise, use a small round file.