I live in Brooklyn, NY and work in New Jersey. Why do I have to pay taxes to both states? In the past I've lived and worked in different states and I've never had to pay both. I've just filed my 2008 return and I actually owe NJ money. Is this right? Please help!

If you are present in a state, then any income earned during this period, must be reported to the state.

To your resident state, you must report your worldwide income for the year.
Read: Your U.S. Tax Return: Working or Living in Two or More states

You work in NJ, so NJ wants its cut of income tax on the wages you earn there, just as if you were a resident. You should make sure your employer is withholding NJ tax from your paycheck to avoid having to come up with a big payment at the end of the year. You live in NYC, so NY want's whatever it can get as well. The only "good news" is that NY lets you take a credit for taxes you have to pay to NJ, so you don't end up paying double taxes on the same income. However, because the combined NY + NYC tax rates are higher than NJ's, you still probably owe some to NY as well.