The answer would be yes if the contract when renting a car allows for it. When renting a car for travel, it must be disclosed to the car rental agency where the car will be driven to before its return to them. If you plan on renting a car to drive out of the state it must be included with in the rental contract. There are some car rental agencies the specifically exclude any interstate traveling with a rental car. It is always best to check the rental car agencies policies before renting a car for this type of travel.
There are rental car places that do allow for state to state travel, but prohibits the car from leaving the country to go places such as Canada and Mexico. Some do however allow this. There are very specific contracts and insurances that have to be paid for this kind of travel as well. The contracts must include the insurance for the country you are planning on driving the car to.
Over all it is not completely prohibited to drive a rental car from state to state. In California, a rental car may be driven to the states along its border without any additional fees or insurance such as Nevada. Often people will rent a car to go to Las Vegas for a weekend instead of driving their own cars. It is a few hours away and Nevada is one of the bordering states for California.
If you are planning a one way trip from New York to Los Angeles there are specific contracts that must be drawn up as well as insurance to cover the car in case of loss or damages to the car in transit. These types of car rentals are not as common and will cost more.