First and foremost, data recovery from a corrupted external hard drive without formatting should be attempted only if the device is still functional and accessible. If the drive is not accessible or does not show up in "My Computer" then the corruption may be too severe to fix without professional assistance.
If the hard drive does show up in "My Computer" but you are unable to access any of the data, there are a few strategies you can attempt to fix the corruption. Firstly, it is always a good idea to check the status of the hard drive in the Windows Disk Management Utility. You can access this by right-clicking on My Computer, selecting "Manage", then selecting "Disk Management". If you can view the details associated with the hard drive, then there is a chance the external hard drive may only require some minor repair. Smaller changes such as file system errors or changes to the hard drive's physical structure can be resolved with Disk Management.
If the corruption is serious, Specialized Repair Tools such as Check Disk (CHKDSK) can be used to locate and repair the damaged sectors in the hard drive. To run a Check Disk command, first open a command prompt window with administrative privileges. From there, type ‘chkdsk K:/f’ where ‘K’ is the letter associated with the external hard drive.
Finally, if none of these methods has been successful so far, it may be necessary to resort to a data recovery software such as Recuva. Data recovery software scans the hard drive to identify data which remains intact and allow the user to select which files can be restored.
In conclusion, a corrupted external hard drive can be fixed in most cases without the need of formatting. The steps above should help mitigate any minor or major corruption problems that occur. However, if the steps do not yield the desired results, it may be necessary to seek professional assistance in order to retrieve any lost data.