To solve a "sticky" door problem, first check the door hinges and make sure they are aligned correctly. Once you have eliminated that possibility then you can try some other tricks.
Another suggestion for fixing a "sticky" door is to fold some sand paper around a wooden block and sand the area around the door hinge that is "catching." Once you have made your edge smooth then you can repaint and seal that area to prevent moisture from warping your wood.
If you have squeaky door hinges it is best to use a spray lubricant like WD40.