I've done this myself a few times accidentally, and have not experienced any problems with the camera or the cards. I think there could be some problems if this was done all or most of the time. Also, if the camera is writing photos to the card when you remove the card, that could cause problems. Thanks.
>If you see smoke coming from the card slots, do NOT immerse >the body in water. > > Also, if you DON'T see smoke coming from the card slots, do NOT immerse the body in water.
More seriously, I don't tend to look whether the camera's on or not when swapping cards, and haven't had a problem yet. I don't swap cards immediately after a frantic burst of shooting, so that may be part of it.
I'm sure I've done this a few times also. I believe turning the camera if is just a precaution for static charges causing small electronic surges that "could" damage the camera and/or memory card.... Small chance but has to be in the manual for cautions and all.
While SDHC cards are hot-swappable, doing so does slightly increase the risk of corruption or damage to the card or camera. Anytime you remove a printed circuit board while power is present on any of the pins, you risk an issue.
Waiting until the camera is shut down also assures that all images have been written do the card before you remove it. If you took a long exposure with long exposure noise reduction turned on, you could run the risk of pulling the card out before the image was completely written to the card.
I just got in the habit of turning the camera off before I change cards or lenses. That doesn't mean I won't have problems, but at least my probability of failure is a little less.
"Red is gray and yellow white, but we decide which is right ....and which is an illusion"