Both light rail and regional rail have flourished in Arizona.
The 
Phoenix
Street Railway offered local service within Phoenix, and ran until a
carbarn fire in the late 1940's.
Tucson today enjoys the Old Pueblo Trolley, running on restored trackage in that city.
Bisbee, Douglas, and Prescott also once had electric streetcar systems. Tempe had a horsecar street railway.
In the early 1900s, both Southern Pacific and Santa Fe offered rail service designed for commuter travel in the Phoenix area.
In 1980, a Salt River Flood Relief train, the "Hattie B.," named for Governor Babbit's wife, was a huge success. See photos and history.
Information on these and other predecessors to modern transportation systems can be found in the Bibliography.