Using ICs from old computer hardware and such
The best way to desolder chips is with a hot air station. However, unless you already have one, the cost will be way way more than any savings from salvaging old parts. Hot air stations are also the best way to hand solder modern fine pitch parts, so that can be a legitimate reason to get one, then also use it to salvage old parts.
The reason a hot air station is good for this is because it can heat all the leads simultaneously. Once the solder melts, you just pick up the part with tweezers.
If you've got a hot air gun kicking around (paint stripper), give that a try. Cruder, huge temperature variance (hot spots), likely to damage parts, definitely lowers the lifetime of the parts, but it is a cheap alternative especially if you don't really care about the outcome.
Chances are that if you remove them with a paint stripper you will not only damage the PCB (bubbles on the surface and copper pealing off) and therefore let off very nasty fumes, chances are you will also damage the IC. Does not mean you shouldn't use a paint stripper for this! I personally use a paint stripper to desolder a few IC's every now and then from boards I don't need, and it works. The IC usually works for me, but I have had quite a bit of practice.
You can use a toaster oven, or just an oven in general for this too. Desolation the electrolytic so they don't go boom when heated, stick the board in. When the board is heating and you think that solder is melted, wait a bit more to be sure that the solder really did melt. Stick your hand in the toaster oven with tweezers or a knife, and a aluminium foil under the board, and simply slide it across the board quickly. Some parts will come off, others will not, rinse and repeat. I would advise against this though, as you put food in there too usually, so unless you have a dedicated toaster oven for this I wouldn't do this. It does give you a much more uniform heating of the board though, and I heard that people just slap the board against the wall of a large bowl and all the parts go flying off into the bowl.
Yet another technique is using special solder. http://www.zeph.com/lowmelt.htm I don't use this because it is expensive (10 dollars per foot !?) It is in youtube though, and people say it works. I suggest you check the youtube videos yourself to make sure it does what it wants.
There are still even more techniques for hobbyists to salvage SMD IC's. QFN is the worst, so I don't usually bother with that anyways. If you have a dual leaded package, put something metal under one of the pins, heat up the lead, and when the solder melts, try to lift the pin up just a bit so the solder is not connecting both, then slide something between the pin and board to keep it separate. Rinse and repeat for the rest of the pins. Personally I have never done this before, but it seems like a good idea.
A hand driven solder pump, like the ones you can get from radioshack for like ten dollars, are a good helping tool in these types of situations, especially for the one I just listed. It will get rid of most of the solder, for DIP it sometimes gets rid of all the solder which is wonderful, and it is very cheap!
You can also try to stick the board onto a pan you don't use anymore (leaded pins will scratch the layer in the pan), and just heat the pan up by putting it on a stove. This does provide a very uniform heating of the board, just make sure that you don't really have any components on the other side!
To use the components if they are not DIP, you can either buy a breakout board ($5 tops), or solder it "deadbug" style. Deadbug is when you flip the chip upside down to give you access to the pins, and then use thing wire like magnet wire to connect the pins to your project. To save lots of time, you can always make a board for it including the required decoupling SMD caps and whatnot from dorkbot or batchpcb or seeed for maybe ten bucks. You do have to wait for the boards, which sucks horribly, but at least you will have a connection to the chip that you know works, instead of guessing if it is the chip is dead, your wiring is bad, or you are using the chip wrong.
Just curious, what IC's do you find on there of use? What motherboards are we talking about? Most if not all components from things like graphic cards and motherboards that I find are of no use to me since I cannot find the datasheet, they have too specific of a function, or require a huge amount of supporting circuitry.