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Here's an easy home remedy, which might give you the desired results. Rub a small amount of toothpaste on the scratch and polish the CD with a soft cloth and any petroleum-based polishing solution (like clear shoe polish). Squirt a drop of Brasso and wipe it with a clean cloth.
Technology to the rescue:

There are many softwares available on the net, which enable the recovery of the CD data. BadCopy Pro is one such software, which can be used to recover destroyed data and files from a range of media.
Just a few clicks is all it requires to recover the disc from almost all kind of damage situation; be it corrupted, lost data, unreadable or defective.
DiskDoctors is another popular company, which offers both software and solutions to recover data from a scratched CDs and DVDs
General Tips:
* Always wipe the CD from the center outward with straight spoke-like strokes. Wiping CDs in circles will create more scratches.
* Do not scratch the graphics layer as you cannot repair the disc.
HINT: Hold the disc up to a light with the graphics layer facing the light source. If you can see light thru the scratches at any point then the disc may be irreparable and or exhibit loading or playing errors.
* Clean your Disc players lens regularly with a suitable product to ensure optimal viewing pleasure.
* Make sure to use a soft, lint-free cloth to clean both sides of the disc. Wipe in a straight line from the centre of the disc to the outer edge.
* If wiping with a cloth does not remove a fingerprint or smudge, use a specialized DVD disc polishing spray to clean the disc.