Some options for renting the Xbox video game console are Rent-A-Center, Aaron's and video rental stores. As of February 2015, it is likely that they will only offer the Xbox One, however.
Rent-A-Center specializes in rent-to-own plans, but someone who only wants to rent the Xbox temporarily could use their "Flex Plan" and simply return the item and freeze payments when done with it. Aaron's stores also lease the console, and they have a similar option that allows users to return it and freeze payments indefinitely.
While many major video rental chains have gone out of business, Family Video is still in business and may have Xbox consoles for rent. Local mom-and-pop video rental stores are another possibility.