You may have a disc, be it music or data, that is scratched and will not read in your optical disc drive no matter what you do to it. Can it be saved?
Possibly. There are a few things you can try to save that disc.
Hardware method: It could be just the drive you’re using
If the disc won’t read in your optical drive, try another one that’s close by. If you don’t have one to spare, try a friend’s computer.
Interesting side note: Older optical drives with slower read speeds have a much higher chance of reading a maybe/maybe-not bad disc than newer drives do because they don’t spin up as fast. Being that laptop optical drives are typically slower, if you have a laptop with a CD/DVD drive, try that. You might be successful.
Software method: Using Nero Burning ROM to attempt a super-slow-read copy
Nero Burning ROM (paid application) has been around a long time and is arguably one of the best disc copying software utilities ever made - if not the best.
If the disc you have will spin up but will not read, Nero might be able to save it or at least at a good chunk of it.
When you copy a disc using Nero Burning ROM (part of the Nero 9 suite), it will first try to copy at the maximum speed possible. When it runs into a part of the disc it can’t read properly, Nero will purposely slow down the drive (all the way to 1x if necessary) and try every single possible way to read the data. If it can’t read the data, it will skip that part and go to the next readable portion and move on.
The disc copy make take a really long time - but you might be able to save whatever was on the disc or at least a good portion of it. If it’s just a portion, better to have something than nothing, right?
I have saved discs with Nero Burning ROM that no other app was able to copy, so I can attest that yes, it does work when all others fail. And if Nero fails.. well.. try washing the disc first (see below).
Physically doing something to the disc: Washing it first
CDs and DVDs are made of two things, aluminum and plastic. The outside shell is plastic, the shiny part is the aluminum. The part that is scratched is the plastic.
Plastic can be washed with just about anything, but the goal is to not scratch it any further.
Paper towels and non-scented ammonia-free glass cleaner (like Windex) do work. Why paper towels and not tissue paper? Because tissue paper is an abrasive and will scratch the plastic surface even worse.
Tip on cleaner used: Do not use anything labeled as a degreaser (like Formula 409). "Straight" glass cleaner is what you want.
Tip on paper towels used: Unscented, plain, no patterns such as Bounty or Brawn.
(Incidentally this is the same reason you never clean eyeglasses with tissue paper because it will scratch those up over time as well.)
Can you read a disc that is physically cracked?
Example: You leave a disc on the couch and forget about it. Later on you go to sit on the couch and watch TV, then…
CRACK!
Uh-oh. You sat on the disc. Very cracked but still together.
Is the disc still readable? Believe it or not, yes - or at least with CDs. A CD which has an "outside in" straight crack in it (from the outer edge to inner edge but not to the center) can be read as long as it’s even with the rest of the disc. However there is the possibility the disc might shatter when in the optical drive. Chances are this probably won’t happen - but it might.
DVDs when cracked usually cannot be read at all. If this happens to you, toss the disc out because there’s not anything you can do about that.
Tip to avoid this scenario: Don’t sit or step on discs (duh).
[Cracked CD photo by hermanturnip]

With the exception of Nero being completed bloated beyond the extreme (especially anything past v7) it’s arguably the best burning application around.
Something else to possibly note: if all else fails - as per above - try and extract the audio into a WAV file on your PC. Quite often if nothing else seems to work when it comes to burning a copy of the disc, digital extraction is almost guaranteed to work. I’ve had discs that looked as though they’d been run over by numerous cars but by extracting the audio digitally to my hard drive, I was able to successfully burn the content to a new CD without a loss of quality.
Just another option to try…
I knew there was a good reason to hold onto a 2000 vintage HP 12x CD burner.
i think i once read somewhere that you can fix a broken/scratched cd or dvd by “polishing” it with toothpaste. Would this work?
The toothpaste trick is not a myth. Ive tried it myself and it worked perfectly. Im not saying it will work every time but it defo worked for me. Just have to make sure the disc is completely clean and dry before putting it into your machine.
yes it will work
Worst case scenario, use Brasso to clean disc. It seems to dissolved the plastic so that the scratches can either be filled, or plastic can be removed to the same level as the scratch.
My experience has been that the disk polishing mechanisms do work somewhat, but I have had to use an additional process after polishing to get it to work. I put a single drop of canola oil on the disk, and smeared it around with a clean fingertip. Then I thoroughly wiped the disk clean with a lint-free cloth. The oil in the fine scratches made them more transparent, like they were polished.