When a private person goes to another Member State to buy goods and transports them back himself (or arranges for this to be done) then he buys at the rate of tax at the point of sale and the result is taxation at 'origin'.
There are some exceptions to this general rule.
Certain non-taxable persons are limited regarding the amount of goods they can buy in another Member State . Non-taxable legal persons, (e.g. Hospitals, Universities, Government departments) must identify for VAT and make intra-Community acquisitions as if they were taxable persons where their purchase of goods in other Member States exceeds a certain threshold.
Individuals living outside the EU, and making purchases while visiting the EU, should inquire about VAT refund procedures at the time of purchase. Member State refund procedures differ, but chances are that forms will need to be filled out when the goods are bought.