I think some people are missing the point, but I know exactly what the OP is talking about as I have the same issue with my WD "My Passport" external hard drive.
Yes; it is powered through the USB. And yes; some USBs don't provide enough juice to power them. But My WD hard drive has worked on my laptop ever since I got it in both Windows and Jaunty. I upgraded from Jaunty to Karmic earlier on this week and the WD passport hard drive no longer automagically mounts.
The drive is connected though as I can see it when I type lsusb into the command line, and I have written an alias to mount it to the same location that it would normally be mounted. But the point is that it is strange that Karmic no longer does what older versions of Ubuntu did!
To make matters more complicated, I have two different computers using Ubuntu - my home desktop and my personal work-related laptop. I upgraded both from Jaunty to Karmic on the same day but the WD passport auto mounts on my desktop but not my laptop and I cannot fathom what the difference is. (At the expense of labouring the point, I feel I have to reiterate that the WD drive would automount under Jaunty but not Karmic so laptop hardware is not the issue.)
As an addendum, as the OP has already said, these WD external drives do make a slight "clicky" sound when they are first connected. This seems quite normal and they do it from day one; an imminent hard drive fail is not the issue.
EDIT: I forgot to mention that this is actually problem I have generally in Karmic with *ALL* external storage devices, including USB flash drives and external hard drives, but again only seems to affect the laptop, not desktop.