I used to get that message all the time, but it's been a while and I'm not sure I remember what fixed it.
1. If you are using a card reader, try uploading from the camera, using the USB cable and vice versa.
2. If you are using the standard file system browser for you OS, try uploading through specialized software (like whatever came with the camera).
3. If you are using Windows, try using a friend's Mac, or the other way around. -- This is a kind of temporary solution, but at least it gives some indication of the problem.
If none of those changes work, I found a site that reviews software written to recover files from corrupt media...
http://www.ultimateslr.com/memory-card-recovery.php
I would be skeptical if there is no demo or trial, but if the photos are really important or you can find a good review of one of the products.....
.... oh here is one that has a trial,
http://www.5starshare.com/Secure_Digital_Card_Recovery-soft48587.html
Of course, if you have a geeky friend, give it to them and see if they can get the data for you!
P.S. I don't know how much general knowledge you have already on memory card use, but the quote:
"I would change items 1 and 2 to say the following:
"Use the camera's format command to delete all previous images. Do not delete any images from the card in any other way."
For item 3:
"Do not make any changes to the card while it's connected to your computer. Let the camera be the only device that makes changes to the card."
From the comments section of
http://theonlinephotographer.typepad.com/the_online_photographer/2007/07/card-practices.html sums it up well. Those tips should maximize the longevity of any memory card, while also reducing MOST problems like this one.