If you have a collection of discs it is almost invariable that some of them will become damaged over time. If your discs do suffer from defects such as scratches, chips, cracks, spotting, or degradation, it may be possible to rescue the data contained on them.
Your first attempts to recover your data should involve a personal attempt to solve the problem. You may spend a little time, but it’s much more affordable to give recovery a shot yourself before paying someone else to do it.
A number of programs have been created over the years which help users of different operating systems to attempt to restore data lost on optical discs. These each work in different ways, but it is very common for very slow low level passes over difficult to read sections of a disc to be used to piece together the data puzzle. When using discs with physical damage (such as cracks or chips), make sure to pay close attention to the recovery process at all times as damage to your drive may result if a disc shatters under the rotational force of the process.
A couple of commonly used Windows programs are CD Recovery Toolbox and Roadkil’s Unstoppable Copier. For linux operating systems ddrescue is a solid option that uses a command line interface. For a variety of Oses (including MacOS) dvdisaster is available, and the bonus for this program is that it can be used as an advanced recovery method, generating data profiles on your media to allow you to have an easier time recovering if anything does happen to a disc after it has been profiled.
Many other options can be found at Wikipedia (some of the programs on this page only deal with non-optical media, so read carefully) or by searching the internet. When using any program, be sure to read the manual carefully in order to give yourself the best possible chance of recovering lost data, and to ensure that you are not attempting to do something the program is not designed to handle.
Professional services can restore from damage of a much more severe nature. Discs that have literally been snapped in half or otherwise shattered can be read by specialized labs. These companies are also your go-to solution when personal computer based solutions fail. Many major cities have businesses that specialize in data recovery. Your search for further assistance should start close to home to save on shipping fees and to minimize potential further damage which can be incurred when mailing discs. If you do not have a good local business, check online for options.
Actual data recovery fees vary widely by the amount of damage, the volume of discs you need restored, and the business you choose. Reputable businesses will offer you a consultation before you pay them. If the company you get in touch with does not, look further.