I have a print of an old painting. If I scan it, is there a program or site which can compare it to old paintings so I can find out what the print is of?

There a Firefox add-on called Tin Eye Reverse Image Search. It's probably available to add to other browsers too.

Once you've added it to your browser, you'll need to add your picture to the Internet somehow (just posting it on Blurtit is enough) then right-click it. From the context menu select "Search Using Tin Eye" and it'll pick up any identical (or similar) pictures.