Pay Income Tax to Non-Resident State?

In the United States, how have others handled state income tax payments when working for a company based in a different state from the one of fulltime, year round residence - having worked at home and never stepping foot in the state where the company is located? I've heard conflicting views as to whether or not I have to pay income tax to the state where my client is located. In this instance, my client's located in California and I live in NY. This is fulltime work so I'll tax someplace! Thanks.