In Denmark, it is not illegal to buy or own counterfeit products for private use, but it is illegal to sell counterfeit products.
You can legally buy counterfeit products from other EU member states online, and you are allowed to bring counterfeit products bought in other EU member states into Denmark.
If you buy counterfeit products abroad or online from a country outside the EU, you should be aware that the Danish tax authorities, SKAT, have the right to seize and destroy the products. You are not entitled to any damages.
You should also be aware that you risk being sued by the company owning the rights to the original product if you are suspected of reselling counterfeit products.
Further information: How to avoid buying counterfeit products
Buying counterfeit products abroad
There are no common rules for purchase of counterfeit products in the EU. So if you travel in the EU, you must check the rules in the relevant member states as the authorities in each member state decide whether it is illegal. You risk being fined for buying or bringing counterfeit products in e.g. Italy.