The French city of Châteauroux offers a good case study:
The motivations for making a transit system free are obvious. Increased ridership can relieve traffic, improve the environment, boost the system’s efficiency, give residents more spending money, help the poor, and rejuvenate central business districts.
Unfortunately, the Châteauroux report contains little large-scale analysis of the effects of the system. But as it turns out, the change nearly paid for itself. Forty-seven percent of bus-goers were already riding for free, and tickets covered only 14 percent of the city’s transit expenses. By slightly increasing the transit tax on big local businesses while eliminating the costs of printing, ticket-punching technology and the human infrastructure of ticket sales, the city turned a profit on the transit system in ’03, ’04, ’05, and ’07. Since ’08, returns have not been as positive, though the report attributes that to a shift in control from the city to the region.
The strategy wouldn't scale for larger cities, but other small cities have had success:
At the end of this year, Tallinn, Estonia (pop. 406,000) will eliminate fares on its transit system for residents, making it the world’s biggest city with free mass transit.
The Dish 