The strange thing is, the power supply should handle power adequately to all the connectors it has for plugging into hard drives etc.
However, I think the main problem these days is from the motherboard connection. There are more and more cooling fans than ever being run from the motherboard. Mine for example has a cpu cooling fan, case fan, 2 graphics card fans.
These and the power a graphics card like my nvidia geforce4 ti4600 can pull can drag a power supply too much. I have seen systems struggle with less than a 300watt power supply but never with 300 and above. I have a 350watt which has never given problems.
Some cheaper power supplies should also be avoided. If you monitor the voltages for these, they fluctuate all over the place. The more stable the psu, the better the system will behave.