I'm planning to take a couple of weeks off when my girlfriend has our baby. My employer is going to let me take this time off, but says I won't be paid for it. Is this legal?
Probably so. In this regard, the United States lags far behind the many other countries that provide lengthy paid parental leave. The federal Family and Medical Leave Act or FMLA gives you the right to time off work -- up to 12 weeks -- for the birth or adoption of a child. But this time off is unpaid. If you absolutely can't go for two weeks without a paycheck, you can use your accrued time off during your leave.
Many states also have some form of a family leave law. However, only a few (California, New Jersey, and Washington (starting in 2012), along with the District of Columbia) offer paid family leave. Except in Washington D.C., this time off is not paid by employers, but from a state insurance program. If you work in one of these areas, ask your employer what benefits are available and how to apply.
Your only hope for more liberal family leave than is allowed by federal and state law is in your employer's policies. But it sounds as if your employer doesn't offer paid parental leave -- which means that you'll probably have to either take unpaid time or use your vacation time if you want this time off.