Florida has been this way for a while, but it's selectively enforced. ALL out of state purchases from a business or an individual to a business or individual in Florida are covered by a Sales and Use Tax (Section 212.06[8] Florida Statutes) and the amount is based on your local tax rate. The base rate in Florida is 6% but some counties are more. If you paid tax to the seller and it was equal to or more than your local rate, you don't owe Florida anything. If you did not pay tax to the seller, or if you paid less than your local tax rate, you are supposed to fill out a form within 30 days and send the form and the money (minus whatever tax you paid to the seller) to Tallahassee.
For automobiles, the same rules apply except that the sales tax is collected when you register it. The tax is based on the amount shown on the sales receipt/bill of sale/title.
There is an exception; if the item you purchased out of state was not brought into the state for at least 6 months after the purchase, then you don't owe the tax.
How do I know this? I purchased about $300 worth of promotional pens from a company in Texas twice and they didn't charge me sales tax. I never really noticed. Several months later I received a letter from Tallahassee informing me that they routinely audit shipments into Florida and identified me as having purchased items from out of state and I owed Florida the tax plus a penalty (10% per month up to 50% max). They kindly agreed to waive the penalty if I paid within 30 days, but they did not identify the purchase or purchases that triggered the audit. After going through 36 months of records I ended up sending them about $42 and that was that.
I guess that is the price you pay for not having a state income tax?