Realtor.com
Realtor.com mostly lists homes for sale, but it also has a section for rental properties. You shouldn't rely on this as your sole source of rental listings, but it's still a good option to consider. Having a feed from every MLS listing service in the country makes it one of the top rental websites.
Any rental property that is listed in the local multiple listing service will also be displayed on Realtor.com. The postings on the site include a wealth of information, making it easy to determine whether or not they are the right fit for you. When advertising a home for rent, real estate agents might specify whether or not pets are welcome.
Website: https://www.realtor.com/