This may be some what of a repetitive reply in terms of my methods for removing scratches. I have posted this a few times to help alot of new members but since it is a sticky now, I will share my success in this regard, once more.
1st of all toothpaste does work pretty good but I have had more success with car polish as TD has mentioned. Simply use an old cotton t-shirt with a small dab of polish/toothpaste and rub it in vigorously until the smaller scratches vanish. Use a back and forth motion when doing this by hand.
As for the difference in my method, I use an electric orbital car buffer with the fluffy buffing pad. I do not recommend the terry cloth buffer pad as it leaves the little circular buff scratches. These pads can be bought at any store which sells orbital sanders. In my case, I bought mine from Sears. Some Big Lot stores carry them for right around $10 (buffer) and $5-$10 (pads) depending on the quanity in the package. If I remeber correctly, it was $5 for one and $10 for three. I use Turtle Wax but just about any polish will work.
The buffer does go in circles however instead of from side to side as previously mentioned. It still works perfectly and because it has the fast rotating motion, does extremely well even for some of those deeper scratches. Just a small dab of polish/toothpaste is all you need. As it spins, it creats a small amount of friction heat and buffs the surface to a new like finish. Depending on how deep the scratches are will determine how long to apply it to the buffer. Just check it periodically.
When buffing, place the buffer upside down so the pad is upright. Then gently with a firm grip, hold the shiny cd/dvd surface to the pad. You may have to rotate occassionally if the scratches are covering the entire disk.
That pretty much covers my tutorial on removing scratches.
Happy gaming and may you never have a problem in regard to scratches ever again.
