There are seven states that have no income tax: Alaska, Florida, Nevada, South Dakota, Texas, Washington, and Wyoming. There are others that only tax certain types of income (a couple tax investment income but not earned income, some exempt retirement income...).
In Florida, the state constitution bans income tax. To me, it doesn't mean much. Government services cost money, and whether the government obtains it from income tax, sales tax, property tax, user fees, or whatever, it doesn't change the fact that services have to be paid for. Only thing it changes is the allocation of who pays what, and what you can do to minimize the impact to you financially.