In general, the requirements for renting a car are the same as the requirements to enter a country. Your passport is needed to enter the country when you are traveling and you will also need it to rent a car.
In some countries, like members of the European Union, a National ID card or some other identification may be sufficient.
Remember that you will need the original identification document, not a copy.
If you are renting in your own country, other types of identification, such as your driver's license, may be sufficient.