We always advise against this. IF a drive fails or starts being problematic, you want to have someone who specializes in recovering data handle the situation. You really only get one good chance at recovering data from a failed drive. YES, we can still try to recover the data after someone else has made attempts, but it just makes the situation much more difficult and complicated.
EXAMPLE: If the issue with your drive is a damaged file system, a Google Search would recommend that you run DSK CHK or First Aid on the drive in order to repair the file system and get access to the data. Although this may work in some cases, most times it doesn’t and it causes irreversible damage. How? If you run First Aid (Mac) or DSK CHK (PC) on a drive that is 100% healthy, the process will go fairly smooth. IF you run it on a drive that has bad sectors (there is no way for anyone to know this until trying the process), these repairs attempts will partially repair the drive and incorrectly alter the file system of the drive. This will cause the data shift and results in X amount of the from the drive being permanently damaged and unrecoverable. We see this problem very often.
EXAMPLE: You dropped your drive, but it still worked after the drop for a couple of days. Then the drive stops being recognized by the computer. If you try to run data recovery software (Google Search Recommendation), chances are high that the read/write heads are going to try and scan the entire drive, hovering over areas of media damage and in the process spreading the media damage throughout the entire drive. Of course the software recovery process is not going to allow you to save the data, due to media damage. At that point, when we receive the drive for recovery, the platters are already severely damaged, and recovery is going to be either very partial or impossible.
IF the data on your drive is important and irreplaceable, please don’t attempt to recover the data yourself.