Bloomberg just published an article that does a state-by-state analysis of state tax burdens.
The 5 states with the highest state tax burdens are Connecticut, New Jersey, New York, Massachusetts, and Maryland (interestingly, all in the Northeast).
The 5 with the lowest burdens are Mississippi, South Carolina, Tennessee, Alabama, and Alaska. Many of these states nonetheless have both an income and sales tax.
Florida (my state) is considered a tax haven because it lacks an income tax and an inheritance tax. It apparently did not make the lowest 5 due to the significant real property taxes collected. The article noted the following about Florida:
Retirees have good financial reasons to flock to Florida. It has no state tax on Social Security, no tax on capital gains, and no inheritance tax. Revenue must come from somewhere, though, so property taxes per capita rank in the nation's top 10. Florida Governor Rick Scott pushed for major cuts to the corporate income tax rate and to state fees during the last fiscal year. The legislature passed more than $300 million of the cuts, including lower fees for a driver's license and car registration.
You can read the full report here.