The number one thing to do is closely inspect the surface of the disk "cookies" for any damage or grime. (You should use a bright light such as a flashlight and look at the surface from an angle) Clean with a damp q-tip if needed. (There are more involved cleaning methods for 5.25" disks, but see what you are up against first.)
Then, as suggested, make sure your drive is in proper working order. Make sure the head is clean, that it can step over all tracks without issue, and that it can low-level format, read, and write to a known good disk without errors.
Consider using a formatting tool other than the DOS formatter. DOS 5 format and later can get hopelessly confused if it sees a non-standard format already on the disk. Other formatters will usually give you more information when things go wrong.
Also, if you format and see some errors, but the disk surface is not falling apart, then try re-formatting a few more times, and in some cases things might improve.
I like to follow up formatting suspect disks by testing the disks with Norton Utilities Disk Test 4.5.
If 5.25" disks are involved, make sure you are not trying to use 1.2mb disks in a 360k drive. Also understand that 360k disks formatted or written to in a 1.2mb drive may not be reliably readable in a 360k drive.