I had the same problem recently and was able to recover all of the pictures from the card fairly easily.
When you say that you plugged it into the computer, I'm assuming that it is the card you are talking about and that the computer has a built-in or external card reader. Having a card reader apart from the camera is essential.
You should first protect your card by sliding the tab to the "lock" position before attempting recovery.
There are various programs available that will attempt to recover the files from your card. The one I used is called Art Plus Digital Photo Recovery (free). It worked well enough but was extemely slow in recovering all photos.
Look on the Download section of CNET and do a search for SD card recovery programs.
Others have had success by taking an unreadable card to a photo lab with a self service digital photo kiosk. The kiosk will sometimes be able to read the card and give you an option to write the photos to a CDROM.
I just have a problem with this 2gb SD card I use for my Panasonic Camera. When I turn on the camera it says memory card error,and when I plug it into a computer neither a Mac or PC will read it. The pictures on the card are really important so I'm just wondering if there is any way to get the data off of it. Thanks