WASHINGTON — Summoning a taxi or car service with your smartphone feels like the future. City governments around the world can agree on that. But many are proposing rules that would run Uber, one of the most prominent ride-requesting apps, off the road.

At a recent conference, regulators and car services from the United States and Europe talked about how smartphone apps are changing the hire-a-car business. Some are integrated with car companies’ dispatching systems, while others allow drivers to directly connect with passengers, phone to phone.