How do states that do not collect state income tax pay for services that other states use tax money to pay for?

Generally it is all paid through sales tax revenues or similar taxes. You will notice that most states that do not have income tax have higher sales tax rates.

ANSWER: The beauty of states that do not levy an income tax on the people is that it demonstrates how unnecessary income taxation actually is. While sales taxes are usually higher in these states these sales taxes can be defeated by simply not purchasing the items being taxed. The Internal Revenue Code makes clear that any attempt to defeat or evade the income tax is criminal and subject to prosecution and conviction leading to stiff fines and/or prison. Of course, that's assuming you are actually subject to the "Personal Income Tax". There are people who are subject to this law and people who aren't. Which are you?