Select cancel to ignore the prompt to format.
Go to "My Computer" / right click drive and select Explore.
If this does not show your files then (if usb or other) connect the drive to a different port.
Try a different cable.
Try connecting to a friends computer.
Use a data recovery company to recover the files.
eg
Data Recovery Service London UK, Hard Drive Data Recovery and RAID Recovery (never personally used them.)
FAT16, FAT32, NTFS data recovery software - do it yourself data recovery and digital image recovery. (is a do it yourself one)
(I do not endorse one particular data recovery company and do not guarantee any success on their part)