Thanks, Ethan. I've been looking for links I could post when people ask this question (over and over). It takes too long to write up an explanation every time.
More to the point, adding to what the article says about jitter, the stability of an audio interface's clock is more dependent on the quality of the PLL (phase locked loop) circuit in the interface than the stability of the source clock itself.
By the time you get through a four foot long word clock cable, the edges of the clock pulses are dramatically rounded and the PLL circuit is having to guess where the start of the pulse actually is. If you have a poor PLL circuit in the interface, your clock jitter will actually be worse with even the best external clock than with the internal clock.
Further, if you have a good PLL circuit that averages out the pulse timing correctly, a crappy external clock will be similarly averaged out, and will end up being just as good as the good external clock... and so will the internal clock....
In short, barring exceptionally bad internal clocks (or devices with separate input and output clocks) on a few cheap/broken-by-design devices, I have a hard time believing that there is any benefit to external clocks. External clocks are great if you have lots of devices and want to be able to keep them all in sync. Otherwise, they are not a good way to spend your money, IMHO.