My mom died in December 2011.
My sister and I have inherited the apartment. My mom was an Italian citizen, my sister and I are USA citizens. We will probably receive each one of us 75.000 Euro as part of this inheritance. Do we have to pay USA taxes on this?
How can we transfer the money from Italy to the USA legally?
Thank you.

The United States government does not have an inheritance tax (a tax payable by the heirs). It has an estate tax (payable by the decedent's estate). Since the estate is in Italy and not the U.S. the estate would not pay U.S. estate tax.
It is possible that whatever state you are in has an inheritance tax and, if so, money received from a foreign estate would be taxable. I rather doubt it because of the relatively small amount you are inheriting, but it's possible.

As far as transferring the money to the U.S. I believe you may have to file some sort of an informational return with the I.R.S.