There are three ingredients in nail polish you should avoid:
Formaldehyde
Used as a preservative in beauty products and known to cause itching and burning (and is classified as a possible carcinogen by the EPA). Countries like Japan and Sweden have banned it completely.
DBP
Or dibutyl phthalate, makes nail polish flexible and exposure to it has been shown to cause birth defects in animal studies.
Toluene
Used as a solvent, is a toxin particularly harmful to the nervous system.
All three of these ingredients score a 10 (the highest) in the skin toxicity database and are linked to cancer, as well as other health consequences. Luckily, there are many brands now available that offer all the pretty, without so much of the toxicity.