I've done both. Desoldered & resused. Also burned parts in the process.
There's no need to get the part off with one hit of the iron. Work slowly removing solder in several stages as necessary, but be quick with the iron heating the solder, not the parts. Use a bulb and braid--each where appropriate. Wiggle or pull parts while heating where necessary.
There's a bunch of desoldering tutorials online, and a few threads dealing with it here. It takes a few different techniques to get off parts with 3 leads, ICs, and other weirdo thngs.
You also need to be careful about electrolytic caps, especially if they're over 10 years old and more especially if they've been out of service for a year or more. Examine them carefully for any leakage or opening of the drain slots. If they look perfect, you might still need to recondition them.