I shall tell you how I rescue components from old circuit boards and store them for reuse. A board from an old (relatively new, that is) hard disk drive shall be shown for an example. The photo (taken using my scanner) shows one such board, after I removed the IDE connector.
Step 1: Desoldering
I have a movie showing my process. I am attacking a tantalum capacitor in the video, but the same process works for all other components too.
First bend a piece of thick copper (or other solderable metal) wire to fit around the component, and contact all its solder pads. Solder it in place. This is done to make thermal contact.
Then heat the wire at a central place with your soldering iron, and lift the component away with tweezers. Or push it away using a wooden toothpick. Only don't be too enthusiastic with the push or it will fly across the room and be lost forever in the crud that covers the (in my case anyway) floor.
These are best stored inside foam cutouts in a suitcase. Miniature, of course.