It should work, and you should be able to make the change but you'll need to check a few things:
*Do you have your install disks?
Windows won't run on a different motherboard without reinstalling it. And when you reinstall windows you might need to reinstall several other programs. Also, if you have Windows 7, check if you have the OEM or Retail version. Microsoft might not let you reinstall the OEM version on a different motherboard. I have Windows XP and I've never had a problem when I upgrade my motherboard. I just have to reinstall each time.
*Do your existing expansion cards (network card, video card, sound card, etc) work on the new motherboard?
Many motherboards have those devices built in, but if you are planning to keep something, make sure you have the right slots. Older computers had an AGP slot for video and PCI slots for everything else. Several years ago they converted to PCI Express slots for everything, also you still need to check their size (PCI Express x16, x4, or x1)
*Does your hard drive and DVD drive have the right connections?
Old drives used to use IDE connections. New motherboards usually have one IDE and several SATA ports so make sure you have what you need of each (you can plug two devices into one IDE slot.)
*Will your power supply be enough? Does it have the right plugs?
Newer motherboards need a separate plug just for the processor, and IDE and SATA drives have different types of plugs from the power supply. You can get plug adaptars to convert from IDE power plugs to SATA plugs if you have enough watts. There are websites that give you an estimate to how many watts your computer will need to run well (though those websites often overestimate).
Sorry that's so long, but I hope I covered everything you may need to know!