Would you be more likely to buy new gear out of state if there was no sales tax

Grannyring, since I don't use Turbo Tax, a question--are you referring just to Federal taxes?  This is a state tax issue.  My accountant's worksheet he sends me has a line item about out-of-state purchases for which I didn't pay tax, and my NJ returns had a spot for it and the detailed explanation and admission I mentioned in the tax form instructions.  Sure wasn't a secret there.

In fact someone I know bought furniture on line from an out of state vendor- spent 5 figures. Sure enough, about a year or so later he got a tax bill for use tax from his own state. Admittedly,,this is the first and only instance of such an occurrence I've heard of, but to doubters, technically, you buy in state, the vendor collects the tax and send it to,the state and if you buy out of state, you collect the tax for your home state and send it to your home state. 

I use Turbo Tax for state tax also. Must be different state to state.

I could not find anything saying it is our responsibility to total up our purchases and somehow pay at tax time.

Bill, Google "sales and use tax" (with the quotes) plus the name of your state. That will lead you to an informational pdf on the subject issued by your state tax authority.

We buy stuff on Amazon etc...with no tax, but must keep track of all these purchases and somehow pay the tax to state we reside in.

BTW, as you are probably aware most of the major online retailers make it very easy to print out a summary of purchases one has made from them during the course of a calendar year. Under My Account/Order History or some such link.

Best regards,
-- Al

I have done this tactic in the past. Absolutely!