The PlayStation 3 uses Blu-Ray discs to hold its games. Blu-Rays hold a lot more information than standard DVD discs, but that doesn't make them any less fragile. Even a small crack in your PS3 game disc will make it unreadable by the console's laser and therefore unplayable. There's a simple fix for minor cracks and scratches, but be warned that these solutions may not work if the damage is too severe.
Wipe the disc down gently with a clean cloth. This is to remove any small plastic shards that may have resulted from when the disc cracked.
Apply a small piece of transparent scotch tape along crack on the labeled side of the disc. This will hopefully hold the cracked seam in place.
Trim off any excess tape that goes over the edge of the disc. The excess could cause the disc to not spin properly.
Squeeze a teaspoon of gritty toothpaste on to the microfiber cloth. Do not use gelled toothpaste, as it does not have the abrasiveness to buff out the scratches.
Rub the scratched portion of the PS3 game disc in gentle circular motions with the toothpaste. You should begin to see the minor scratches fade away as you wear them down. Continue until the scratches have been removed to your satisfaction.
Rinse the toothpaste off the disc under cold water and dry it with a clean towel. Test the game out to see if your fix worked.
Sometimes games are just too damaged to fix. Using a severely cracked game in your console could potentially damage its internal components, so be careful when testing them out. Though toothpaste is probably the most readily available substance you have access to, other abrasive chemicals are also effective.