To recap from the bits sprinkled through the previous thread, those little handheld $10 desoldering pumps you buy at Dick Smith or Jaycar seem largely useless.
Most of the stuff I do involves through hole rather than surface mount. My preferred technique at the moment is to use desoldering braid. If I don't care about the component, the quickest / safest way to remove it is to cut the pins, remove the chip body, then quickly remove the pins from the board and clean up the pads with desoldering braid. That gets the component out fast, and minimizes the risk of damaging the PCB. Of course, it means the component is toast. I can usually get through hole components out in one piece with desoldering braid too, but it takes a long time, and you put a lot of heat into both the component and the PCB.
I would love a decent and inexpensive desoldering gun. Carcenomy said he has a good clone of a Hakko 474 which he bought for about $250.
natshaw is about to try some $50USD tool off eBay which SpidersWeb didn't think was great.
I have seen some people rave about cheap little tools like this Radioshack one before which is about as brute force as you can get for $13USD

http://www.radioshack.com/product/index ... esoldering

What about something like this? (Approx $80-$90USD on eBay)
http://www.ebay.com/itm/251191119518
How about you guys? What are your preferred tools, tips, and techniques for quickly removing components without damaging them or the PCB?