All the windows were painted shut when we bought the house. The bottom sashes were easy to get open by just gently removing the sash stop after first scoring the paint with a utility knife to help eliminate paint chips. Once the sash stops are removed the sash is free to go up and down.
If your sash is just stuck in a few areas and not entirely painted shut you can buy a tool that looks like a pancake turner with little sharp points on the flat part and a saw blade cut out around the edge. You wiggle this tool between the sash and the sash stop to break the paint free from the sash.
I was able to move two of the top sashes back up into place so that the sash was no longer crooked in the opening. That always bugged the heck out of me.
Over the years I have made all my bottom sashes operational but I want and need the top sashes to also work. Why have double hung and only use the bottom sash? If you lower the top sash a little and raise the bottom sash a little you can get great ventilation because the warm air rises and goes out the top and the cooler air comes in through the opening at the bottom.
An operational top sash also works well during a rainstorm if you have an extended eave. By closing the bottom sash and lowering the top sash you can have an open window without the rain coming in, unless of course it is straight line rain then just close the windows and head for the basement.
While I was at it, I also removed any loose glazing compound. Seriously, glazing compound whether removing it or installing it, is one of the most tedious jobs. When I had my first house, I spent an entire summer just reglazing the windows and repainting the exterior of the sashes. It looked great when I was done but that was many years ago and there is now no way I could stand on a ladder for that long. Just the thought of it makes the bottom of my feet hurt.
Two days ago we installed the 1 1/4 inch square piece to fill in between the drip edge and the trim board that we added to the peak before we finished shingling. It worked out perfect. I primed and painted the pieces before R installed them so I will only need to touch them up when I paint.