What countries need covid PCR testing for travel to enter their country?

There are 2 different categories of COVID-19 test:

Viral test: detects whether an individual is infected at the time of the test. The most common type of accepted test for travel is PCR.
Antibody test: detects whether an individual has been infected in the past

Travel information if you’re vaccinated:

https://www.afar.com/magazine/travelers-with-covid-vaccines-can-visit-these-countries

WHICH TYPE OF COVID-19 TEST IS REQUIRED TO TRAVEL TO EUROPE?

To travel, a viral test is needed as it is important to know whether someone is currently carrying the virus. Within the viral category there are then 2 types of test:

Nucleic Acid Amplification Test (NAAT): detect genetic material and are usually more accurate but results can take longer
Antigen test: detect viral proteins and are generally less sensitive, but results are available more quickly.
PCR testing for travel to Europe are the most widely accepted given their increased sensitivity and ability to pick up even small amounts of the virus.

For country specifics:

Sweden, Netherlands, France, Italy, Belgium, Austria, Germany, Spain, Denmark, Switzerland, Finland

Reference: https://www.etiasvisa.com/etias-news/pcr-covid-testing-travel-europe

United Kingdom

Effective August 2, vaccinated Americans can enter England, Scotland, and Wales without a mandatory quarantine, the British government announced on July 28.

https://www.afar.com/magazine/travelers-with-covid-vaccines-can-visit-these-countries

Hawaii

Hawaii has ended its pre-travel testing and quarantine requirement for domestic travelers if they’ve been fully vaccinated for Covid-19 in the United States.

Reference:

https://edition.cnn.com/travel/article/hawaii-travel-covid-19-need-to-know/index.html