The Department of Justice (DOJ) has specifically stated in rulings that websites should be designed so they are accessible to individuals who have vision, hearing, and physical disabilities. There’s a growing body of case law where the DOJ required companies to provide an ADA compliant website and levied hefty penalties when sites failed to measure up.
Title III also has applications to existing facilities. One of the definitions of "discrimination" under Title III of the ADA is a "failure to remove" architectural barriers in existing facilities. See 42 U.S.C. § 12182(b)(2)(A)(iv). This means that even facilities that have not been modified or altered in any way after the ADA was passed still have obligations. The standard is whether "removing barriers" (typically defined as bringing a condition into compliance with the ADAAG) is "readily achievable", defined as "...easily accomplished without much difficulty or expense".