Freeing a Stuck Window
Wooden sash windows (two windows that slide up and down, sometimes called double-hung windows) and casement/awning windows (windows that swing outward on hinges) are the most likely types to become stuck. They're especially vulnerable to having the wood swell during humid weather or to being painted shut.
If you've just moved into the house, check that the windows haven't been nailed shut. If they have, use pliers or a small pry bar with a nail puller to remove them. Work gently, using a piece of scrap wood or cardboard under the leverage point of the pry bar to avoid damaging the window sash (the frame around the glass) or the stop (the piece of wood trim that runs up the window frame on the wall, forming a neat seal against the sash).
Newer sash windows use springs for smooth operation. Examine the channel that runs up and down beside the sash (called a track insert) to find the adjusting screw. Turning the screw will change the spring tension, allowing you to choose the best setting.
Breaking Through Paint
To break a paint seal, carefully run a utility or putty knife through the paint where the window sash meets the stop and the windowsill. (Tap the knife with a hammer to penetrate the seal.) Repeat this on the house exterior if needed. If that doesn't work, place a piece of wood against the sash to protect it, and tap the wood lightly with a hammer, or, working from outside, try to insert a thin pry bar between the window sash and the sill to break the seal.
Keeping Windows Moving Freely
Windows that are sticky, rather than completely stuck, may need to be removed so that you can clean the channels in which the sashes slide up and down. Excess paint can be removed with paint thinner, steel wool, or sandpaper, and rough wood can be sanded smooth.
If the problem is high humidity that's a persistent characteristic of your weather, try sanding the window sashes and the channels/trims wherever the two surfaces meet until they move freely. Follow up by sealing the raw edges with paint or varnish to prevent the wood from absorbing any more moisture. If the humidity's temporary, wait until the window operates freely again, and then seal the window sash edges and channels or frame with paint or varnish. Rubbing a wax candle along the channels or trim and the window edges can also help.
When the Stop's the Problem
Sometimes, the window stops can bind against the sashes. If this is happening in one isolated spot, you may be able to move the stop by placing a block of wood against it and tapping the wood with a hammer in the direction you need the stop to move.
Otherwise, remove the stop completely, and reposition it. (Scrape off paint edges as needed to ensure that the stop sits flush in its new position.) Place a thin strip of cardboard between the window sash and the stop, to ensure that you're giving the window room to move, and nail the stop into place.