Polish With Paste
Renters take note: You may avoid move-out fees for any minor scratches in window glass by buffing them out yourself before your lease ends.
It's likely you already have what you need for the job: A toothpaste that contains baking soda, or any non-gel toothpaste, is the best for polishing out tiny scratches. And the technique is simple -- you'll need clean windows, a tube of toothpaste and three clean cloths. Apply a small amount of paste to a soft cloth first, and gently rub the scratch (a circular motion is best) for about 30 seconds. Wipe the area clean with a damp cloth and dry it with a lint-free cloth [source: Luttschyn].
Baking soda can be used as an all-purpose, non-toxic cleanser, and because it's is a gentle abrasive it could be used instead of toothpaste -- just mix up a thick paste (about 3:1 baking soda to water), and use as above.
Buffing is also important for removing any tough stains that may have accumulated over the years.