I'm having an interesting variation on this problem. I bought a Western Digital Passport Essential 500GB portable HD two days ago to take with me on a trip. Up until this point, I'd never had any problems with either USB port on my MBP, and I bought mine in 2006. I plugged the drive into the right-side port, it mounted just fine, and I was able to use it just fine for a day or so.
Yesterday, I installed Apple's latest security update, restarted the computer with the drive still plugged in, and it didn't mount. I unplugged the drive and got the "The device you removed was not properly put away" message, so I plugged the drive back in to the right-side port. My computer immediately shut off without any kind of message or warning, so I restarted it with the drive plugged in to the same port. It took at least a minute, but the drive mounted, and I was able to use it. I tried re-formatting the drive, ejecting it, and plugging it in again, and the same thing happened: complete shutdown, no warning at all. Then I tried the drive in my left-side port, near the power adapter, and haven't had any issues at all, mounting or otherwise. I'd really like some help understanding what's going on here, is it an issue of too much power draw, or what?