Homes for Rent in Burlington, KY. Maybe youâre tired of apartment living, maybe you want more space, or maybe youâve just always dreamed of living in a house. Whatever it is, youâre looking for houses for rent in Burlington to find your next home. A rental house is the perfect place to make your own, with plenty of space for your family to grow. With hundreds of thousands of active listings all across the country, Apartments.com can help you find the perfect KY house for rent near you. Click on any rental house listing to find out more about the neighborhood, house features, nearby transit, parking, and more. Take a look at photos, too, and start envisioning how youâll make your new Burlington rental house into a home. Let ...