Well, we've all been here at least once in our lives.
Our favorite CD, be it music/movie/game/whatever, will no longer play. It's scratched beyond all repair and needs resurfacing.
Well, hopefully this will help you as it has saved me countless times when getting second-hand/used game discs. This is ONLY A LAST RESORT. I do not advise doing this unless you are unable to read/use the disc.
What you will need:
* Mr. Clean Magic Eraser (I'm sure other brands work, I'm using this brand for this post)
* Scratched CD
* 15 minutes of your time
My sample is using a copy of Aggressive Inline for the PS2 (I love this game).
To validate results, I'm using a copy of IMGBURN to make an ISO image of the disc (my PS2 is hooked up in my SUV, I don't feel like bringing it in the house right now). Please be aware that I do not condone piracy / backups / etc, and I am only doing this to validate results.
Here is what I'm working with. Disgusting isn't it? Imagine one of your favorite games in this condition!

I attempted to do a backup of the disc while it was in this disgusting shape... it failed. No surprise there.

Well, time to cure this monstrosity. Or at least, make it a little better. Wet your Magic eraser like you would when cleaning anything else with it, then place it on the CD and go from the center of the disc to the outer edge a few times. Slowly rotate the disc and repeat this motion just like you would if you were cleaning it.

After using the magic eraser to sand the disc (that is essentially what you are doing), you can fix a lot of the issues. Obviously, you can't keep doing this forever, but it will help recover discs you thought were unrecoverable.
Here is the same disc after about 5 minutes of work.

It looks way better. Not perfect, but much better. It even backed up to my computer just fine. I tested the image in an emulator to make sure it worked, but I won't share the details on that here.

So to all those out there with unreadable or heavily scratched discs, I hope this helps you out.