Using an adapter to go from an old 20 pin power supply plug to the current 24 pin layout is not a good idea. This can overload some of the pins on the plug. From <http://www.pcuser.com.au/pcuser/hs2.nsf/lookup+1/BD49CA5565DC5759CA25714100137F7B>:
Before anybody goes using a 20-pin to 24-pin adaptor and an older ATX power supply with a newer motherboard which requires a 24-pin connector it'd be best to sit back and reflect first on just what the system actually is. If the system is a rather basic home or office productivity system, with not a lot of components installed or peripherals connected to it, then you might get away with using such a configuration. The 20-pin to 24-pin adaptor provides an additional 12 volt supply to the motherboard by 'splitting' the 12 volt line. (In other words, the extra leads are there for a reason.)
But if the system is a high performance gaming system, or perhaps has lots of components installed, or a highly demanding graphics card installed, or maybe a number of USB devices regularly connected and drawing power from the motherboard, then the adaptor will NOT be a good idea. In such situations it would definitely be best to replace the old power supply unit with one which is more suitable.
Remember, wattage rating isn't enough in itself when it comes to power supply units. The unit needs to be able to deliver stable voltage levels, and adequate amounts of power to the places where it is needed. The 12 volt 'rail' being split in that older 20-pin unit may not carry enough power to cope with the increased load placed upon it.