Check caulking around window where it meets the sill and the trim, both inside and out. Check caulking around trim where it meets the wall. Remove any old, damaged caulk. Re-caulk all seams.
Windows Stuck Shut
If you have older, painted windows they may be painted shut. Go around the edges of the window sash where it meets the frame with a utility knife or scraper and try to release the paint in those seams. If that isn't the issue, check for obstructions or issues with the tracks on the inside of the frame and check for proper functioning of locks and hardware.
Doors Rubbing or Sticking
Doors can often become warped over time and with weather changes. In addition, door frames can shift or loosen, which can cause the door to stick or rub against the frame when operating. Check the door slab and the frame for plumb and level. If everything is plumb and level, you may just need to shave the door a bit. You can use a hand planer or power planer to shave some off of the door in the problem area. If you need to adjust the frame, get a tapping block and try to tap the frame into proper position with a hammer. Once adjusted, Insert some nails or screws to hold the frame in it's proper position. You may just need to tighten the screws in the hinges or replace with new screws. If the hinges are pulling away from the frame or the door, it will cause problems. Try to tighten the screws first. If they won't grab, you may need new screws and/or some fill for the screw holes in the hinges.
Utility Bills Higher Than Usual
If you notice that your recent utility bills are higher than usual, you may have some energy efficiency issues to address in your home. Some are very simple, others require more work. If it's a heat wave in the summer or a real cold spell in the winter, it could just be a normal increase in your gas, oil, or electric bill based on the extreme weather. However, you should check the efficiency of all your HVAC systems and any areas that could be letting outside air into your home. You may have drafty areas around doors or windows. They could just need some caulk or weatherstripping to seal them better. If they are older, you should examine the framing and door/window to see if any repair or replacement is needed. A damaged or worn kerf seal around your exterior doors is a common cause for drafts. They can be purchased at home centers for about $15 for a full door frame and are very easy to replace.
Drafty Door Corners
The exterior doors in your home can be prime places for drafts to enter, which affects the temperature of your home, especially in the winter and summer. This will have a big impact on your comfort and your heating/cooling bills. The most frequent place for air to enter is in the upper and lower corners on the latch side of your doors. Doors should have an adhesive weatherstripping pad in both corners to help seal the gap. If not, you can purchase them and stick them to the door in those spots. Also check the kerf seal around the door (soft seal around the sides and top inserted into the door jamb). They can be replaced easily and cheaply. Lastly, check that your door is plumb. Look at the gaps up and down both sides of the door between the door and the jamb. If it is uneven, you may need to shim a hinge at the top or bottom to straighten it out and close the extra gap in one of the corners. You can use regular wood shims, but you can also buy plastic hinge shims made for that purpose.