Doors have stopped closing due to humidity, how can I close my doors?
First things first: Check to make sure the screws in the hinges are all tight. If they are not, you can pack the screw holes with toothpicks and white glue, and once dry, redrill and reset the screws. 

Next things next:  Assuming that the hinges of the doors are properly mortised (set into the wood), that the door has not sagged on its hinges (a different question), and that there is no significant bump in the frame, the best bet is probably to trim down the doors and then properly seal them to prevent moisture absorption.

There is supposed to be a gap between the door and the jamb (the broad moldings that face toward the door opening). This gap should be about the thickness of a nickel (but a good bit larger at the bottom) when the door and framing is at its tightest (in high humidity). Doors and their frames shrink and expand naturally, and sealing (with paint/varnish/poly/etc.) is meant to minimize, but not eliminate this shifting. Once you have a sticking point (assuming the hinges haven't shifted much) you need to re-size the door.

Sanding may be sufficent, but you probably need to take off at least 1/16th and preferably 1/8 to solve the problem long term. In most cases it is worth taking the door down so that you can work flat and exert some pressure. Befor taking it down, mark the tight spots with a pencil line run parallel to, and about 1/8 in from the jamb. Then pull the hinge pins and set the door standing on its hinge edge down. If you need to work near the lockset, you may need to pull the latch bolt and its faceplate, or the whole lockset if it is a mortise lock. Either way, you need to remove the door handles and the spindle. 

An orbital finish sander may do it, but this may be too slow. Careful use of a belt sander may be preferable. But careful. A plane or Sureform-like tool can remove a fair amount of stock without much risk of serious gouging.

Check the door regularly by resetting it on its hinges. Be generous with your trimming. It is hard to over-trim and you don't want to be doing this again.

Last things last: Once you are certain of the fit, take the door down again and SEAL IT! Prime and paint all expose wood, or stain and topcoat if using clear finish. Let it fully dry. While it is down, check to make sure that both top and bottom of the door are sealed.  This is often the most frequent source of the moisture that causes door to swell.

P.S. I learned these lessons the hard way, having installed several doors on a basement project (read soon to be damp) in winter where the gapping was not quite sufficient and the sealing was less than complete.