I live in Florida, but work in other states throughout the United States. My employer only takes state taxes for New York. Is this correct? When I file with New York I never get back everything I paid in because I live in a state without state income taxes.

If you are present in NY to work, you will pay NY state taxes. If you are not present in NY to work while your employer is in NY, you do not pay NY state tax.

Note that you should be paying NY state taxes ONLY on the income earned while working IN New York.

You also have a legal obligation to determine if you owe state income taxes to other states with state income taxes. It is likely that the amount earned in those states is so low that there is no tax obligation, but you need to make that determination for each affected state.

Highly paid professional athletes have similar problems. They must often file state tax returns for over 20 states, because their per-game income is usually quite high and well over the minimum taxable pay for the specific states.