The method we used at work for anything up to a 16 pin IC was basically the same as hadron's. Our soldering iron tips were a little more professional of course; we used Hakko's K(knife)-type tip.
We’d dollop some solder across the blade, and run the blade back and forth across one side of an IC till all the joints on that side were melted. Then we’d do the same on the other side, and quickly return to the original side to repeat the process again. If all went well, by this time both sides were hot enough that all the joints on the IC were still melted. All that was needed to remove the IC at this point was to lift the blade; surface tension would carry the IC along with the blade.
The K-type tip is also probably the best tool for removing chip type parts like resistors and capacitors because you can apply heat to both sides of the devices at once. You simply put a bit of solder on the blade, and lay it across both pads of the PCB and slide the blade to the side. Surface tension does the rest.
Once you get used to using the K-type tip, it’s faster and more consistent than using SMD tweezers, which are near useless when they wear out even a little. This is of course only true for smaller ICs, but the K-type tip definitely has its place.
The K-type tip is also my favourite tip for soldering SMD ICs. You put a bit of solder on a corner pad, align the IC, and solder that corner pin to properly position the IC. Then you feed solder to the blade while running it along the IC legs, and then pull the tip away. The large surface area of the tip does a great job of pulling off excess solder, so the amount of solder you use becomes largely irrelevant. Using this method, you get perfect joints pretty much every time. You should be able to solder anything down to QFPs with this technique, though these require a bit more care.
*edit* Please be aware that this desoldering technique requires a lot of practice. At first your movements are clumpsy, and you end up applying too much heat. When you finally do remove the IC, you end up splashing solder all over the PCB. Find junked boards at any place you can, and practice. A lot.
*edit ends*