Is there any way I can transfer data from an ancient unformatted floppy disk without damaging any of the content?

Your best bet is to talk to someone at Best Buy (the geek squad) or something. If they can’t do it, they can probably direct you somewhere that can. Be VERY careful with the disk. Keep it away from magnets including your phone and your laptop. Try to keep it dust free too.

Also, just to control your expectations, there is a good chance its been corrupted by now. Depending on how old it is, its possible its been near a magnet or something else that would mess it up. If you do get the data off it, go through and make it makes sense.

If it’s not formatted, there’s no data on it.

If you have old disks with data, then it depends. You can buy external USB 3.5” floppy drives. But for older 5.25” floppy drives, external USB drives aren’t made, so you’re SOL.

@HungryGuy I remember transerring some files onto it a long time ago, but now when I put it in the PC, it says it’s not formatted. What does that mean?

A professional will be able to convert it for you. Do a web search for data conversion.
P. S. unformatted means it contains zero data – formatted means it contains data.

@queenie – That means the disk has gone bad with age. That happens with floppy disks. As @YARNLADY said, there are data recovery services that may be able to get data off an old floppy. But they’re expensive to use. Also if the disk has gone so bad that it’s reported “unformatted” there’s likely data errors on the files on it. If the files are text files, you can edit them and fix the errors yourself. But if they’re binary files, then again, you’re SOL.

Okay, thanks everyone :)

The floppy is not actually unformatted, but either the format is one that your PC does not support or the filesystem is corrupt. Unfortunately the latter is more likely. Floppy disks are not a good long-term storage medium.
If you want to try to save it yourself, I recommend getting an Ubuntu live cd and booting your computer from that. Put the disk in the drive and see if Ubuntu recognizes it. IIRC Ubuntu supports all MS-DOS and Windows file formats “out of the box”. If Ubuntu is able to recognize the disk, then you can open it and save the data you want to a hard disk or CD or whatever.
If Ubuntu does not recognize the disk, you can try using the Disk Utility (it’s in the menus under System->Administration->Disk Utility) which might see the disk even if it doesn’t auto-mount.
If that doesn’t work, you can use the “dd” command to make an image of the contents of the disk regardless of filesystem corruption or other concerns. If the data on the disk is important to you then I recommend this step to preserve the information from further degradation as the floppy disk ages. Save the image somewhere safe, and when you try to recover the data, use a copy of the image and not the disk itself or the original image.

Thanks a tonne @koanhead. I’ll try that out :)

@queenie Stop, don’t try that. I’m sure what @koanhead said is correct, but if you mess it up, you might lose everything. If the data is worth saving and you have the money for it, go to a professional. Believe me, I’ve tried before and lost a lot of stuff.

@roundsquare Okay, I won’t. Thanks.