Surface mount resistors and capacitors come off nicely with two soldering irons.  That's why you see a pair of them at my bench.
Removing chips with many pins requires more sophisticated and specialized equipment.  I didn't want to spend the money, either.  So I just slice the dang chip off with a razor blade.  In fact, I sometimes do the same with a DIP package.  On a multi-layed board, those pesky ground and power plane connections make it hard to desolder.  For me, I just waste the chip, in return for preserving the board.  Removing pins one at a time is a lot easier.  My technique is to add solder, not remove it.  Get solder and flux on that pin, heat it up and pull out with a small pliers or nippers.  More solder, not less, is the key to prevent damage to delicate pads and traces.
jh