I think that depends on the brand of nail polish somewhat.
Some are alcohol-based, others use acetone as the solvent
(the liquid used to dissolve the polish) which is slightly more
toxic. Harmful? No, I don't think so. At least most
people who use it don't seem to lose fingers from it...
A really good person to ask is a manicurist, who works with
nail polish all day long. Also, you could buy a bottle
and look at the label, then go to the library and start
looking up the components listed on the label. Finally,
try writing to the manufacturer to ask what the ingredients are.
If you go to a place like The Body Shop, they have complete
information on their products.