State and municipality bonds are sort of like U.S. Treasury bonds, except they're issued by a state or local government. They pay a fixed interest rate, but your interest is usually tax-free.
Of course, they pay a lower interest rate than taxable bonds. Thus, the only reason these tax-free bonds would be better than taxable bonds is if you are in a high enough marginal tax bracket to compensate for the difference in interest between these tax-free bonds and taxable bonds.
An example should make this all clear. Assume you have a marginal tax rate of 40%. (You earn a lot of money.) If you invest $100,000 in a typical taxable bond that pays 10%, each year you will get $10,000. But subtract out the 40% tax, and you are left with only $6,000 after-tax.
Compare this with what would happen if you invested that same $100,000 in a tax-free state bond. This bond only pays 8%, being tax-free and all. Each year you get $8,000. But you pay no tax, so you are in fact better off than if you had bought the taxable bonds!
Now, lets change your marginal tax bracket to 10%--you don't earn much money, so your marginal rate is low. You invest that same $100,000 in the taxable bond that pays 10%, you will get $10,000 pre-tax but only pay your marginal rate, 10%, on that sum, so you are left with $9,000.
With the tax-free state bond at 8%, you only get $8,000, though you don't pay any tax on it. So at your low marginal rate, you would have been better off buying the taxable bond.
My point is, tax-free bonds are probably only useful if you earn a lot of income each year to put you in a high marginal rate.
Source: I'm a law student and we learned about tax-exempt state/municipal bonds today in Tax!
Municipal bonds, loans to your local government are free of taxes (both state and fed). I have excess cash that would normally be in certificate of deposit in muni bonds currently making 3% tax free. There are risks, best to consult with a money manager if you are uncertain on how to gauge the associated risks.