A bus service (AirRide) connecting Ann Arbor and Detroit Metro Airport offers an inexpensive and convenient alternative to the shuttle or cab service. Reservations are encouraged and it's cheaper if you reserve ahead. Information about the service can be found here:
For reservations, click on the "Book Now" box at the AirRide page. One carry-on bag, one personal item, and two checked bags are free. The service runs 7 days per week and about twelve times a day.
A few notes about the service:
Finding the Bus at the Airport
At the Airport, follow signs for Public Transit. AirRide bus stop signs are posted at the Lower Level at International Arrivals (McNamara Terminal) and at the north end of the Ground Transportation Center (North Terminal). Your itinerary (it is recommended you print this out when you've made your reservation) will also have details about where to locate the bus.
Bus Stops:
http://www.myairride.com/AirRide/BusStops
When coming to Ann Arbor, the first stop will be Kensington Court Hotel, which is near the intersection of Interstate 94 and S. State Street and near Briarwood Mall. If you want to stay on the AirRide bus, it will take you to campus or on to downtown Ann Arbor.
Schedule
As you're booking your flights, you may want to take the bus schedule into consideration. It comes from the airport almost every hour from 7am to about 9:45pm and goes to the airport almost every hour from 5am to about 7:45pm. Check the schedule here:
http://www.myairride.com/AirRide/Schedule
Just a cautionary note, there is an AirRide Bus that goes to Michigan State University in East Lansing also - be sure to get the University of Michigan (Ann Arbor) bus!