Most major cities have at least one company that runs an airport shuttle service between the airport and hotels. The majority of them either can provide accessible service or will provide accessible alternate service. Another way to find out who these companies are and how to reach them is to inquire at a hotel in the area. They may not know if the company provides accessible service but they will know who they are and how to reach them. A good resource for finding transportation options that is often overlooked is the Center for Independent Living in that city.
Most cities have one and they all have an information and referral person.
These organizations are a wealth of information about all types of services for people with disabilities. They often can put you in touch with transportation options that are generally used by local residents, but that can be utilized by visitors. Another often-overlooked option is the cities public transit system or their paratransit system. In the fourteen years that I have lived in Denver I have never been on a public bus and have only used the light rail system once. However, I have found it to be a good source of economical transportation when I'm traveling.