The general rule is you pay tax to the non resident state on the income you earn there. You also pay tax on ALL your income to the resident state, but get a credit (or partial credit) for the tax you paid to the non resident state.
But it depends on the circumstances and the states. Man neighboring states have "reciprocal agreements" on wages, and it is not necessary to pay tax to the non resident state.
Also see this about business Trips. http://money.cnn.com/2013/06/28/pf/taxes/business-traveler-tax-threat/ If you live in a state without an income tax (e.g. FL or TX), it’s more likely you should file in the work states. You can't use the "it all comes out even" rationale for not filing.
