First, only PCI-E video cards require the special connector. The motherboard itself uses a standard ATX connector, with the now-standard extra 4 pin connector.
Second, there are adapters that can convert a normal Molex (aka 'device') power connection into the PCI-E video power connector.
So, in all likelihood, you will not need a new power supply. But, if you want to run high-power-use devices, and your power supply is more than two or three years old, make sure it can handle the load.