It depends on the Garmin device you have. Some of them you can view the files from your computer, while others you can not. I have had this happen several times. When it happened to me there was a corrupt file which was preventing the files to be transferred off the watch. If you can plug the Garmin device into the computer and see your activities you are good, copy the files off the device to your computer and upload them manually to Garmin.
If you can not connect the Garmin to your computer and see the workouts, you are going to have to delete one activity at a time from the watch until you find the corrupt workout. I would say start from the oldest to the newest, but I would be guessing.. I would just start with deleting one at a time until you find the corrupt one. Once you find it, the rest of the files can be copied. It sucks... but I don't know of another way to get them off. If you delete all of them and it still doesn't work. do a factory reset on the device.
Good luck!
Jeff Dell
Endurance Tracker - For the data driven athlete.