Sometimes it works, sometimes not. Officially, the added 4 pins are supposed to support the PCI express graphics slot. I ran a TForce 6100 socket 754 mobo with a 20 pin PSU connector without incident. Of course, I was only using the integrated graphics at the time. Your best route is to try it and see. It should not harm the mobo or the PSU by trying. If it fails to boot or is unstable, you can buy a 20 to 24 pin adapter to take care of the issue. Note that an adapter potentially puts more current through a couple of the wires in the 20 pin PSU connector that could cause an overload in the wire, melting the insulation which could cause a fire or short out the PSU and/or other components. Careful consideration should be given to the amount of power your computer will likely consume through the appropriate voltage rails to determine if you would be at risk when using an adapter. If you have any doubts as to the safety of adapter usage, you should replace the PSU with one that has a proper 24 pin connecter.
Everything's been said, but just a few details that might interest you.
Lower power systems generally do ok with older 20-pin PSUs (atx 1.1)
I'm running a socket 775 asus M-ATX motherboard with a slightly overclocked 3.2Ghz Celeron D, using an old 300W thermaltake PSU (20 pin) as a file server. Nearly 1 year of 24/7 operation and no stability issues so far.