An Intel desktop mainboard has a Socket 775. This socket was introduced in early 2004 and supported Celeron and Pentium 4 family chips based on 90 nanometer technology. It survived through the transition to 65 nanometer and now 45 nanometer CPU families. It supports single, dual, and quad core chips. The desktop AMD CPU chips use an AM2 socket that has recently been upgraded to something called AM2+.
Although new CPU chips will fit in and old socket, there is more to support than that. Each new generation of circuit size runs at a lower core voltage, and the mainboard has to recognize the CPU chip and give it the right voltage level. New boards know all about the old chips, but each time Intel releases a new CPU chip even the most recent board may require a BIOS upgrade to recognize it.
There are some tricks a mainboard can use to support an unknown CPU chip. If it does not know the correct clock speed, for example, it could always choose a very low clock (say 100 MHz) that is just enough to bring the system up to the point where the user can run the BIOS configuration panels and set the correct speed manually. However, many boards will simply refuse to power up if they don't recognize the CPU chip.
This is why it is helpful to keep some old Socket 775 Celeron or Pentium 4 chip (and heatsink) you took off the system you threw out a few years ago. If you buy a new mainboard and CPU, but the mainboard requires a BIOS upgrade to support the new CPU, then you can plug the four year old CPU chip into the socket, power up to the BIOS screens, and then flash a new BIOS that you downloaded on another system and stored on a USB memory stick. Once the latest BIOS is installed, then you replace the old CPU with the new one you just bought.
Unfortunately, there are some problems that cannot be solved with software. The latest AMD Phenom Quad core processors draw 125 watts of power at full load. That turns out to be more power than even the most modern low end (less than $100) mainboards can supply. The mainboard blows out like an overloaded fuse. Even the dual core models of the latest CPU chips may require a new board with an AM2+ socket and may not upgrade older AM2 boards.
Each vendor has a Web page for each board that lists the processors supported by the board and the required BIOS level for that processor. Before you buy anything, make sure that the board and the CPU chip are compatible, and if a BIOS upgrade may be needed, line up an old CPU chip and heatsink that you can borrow if you need it to do the flash.