Congratulations to Los Angeles Metro, the latest transit agency to make connections (also called transfers) free. There are footnotes: you have to be using a smartcard, but if you're in Los Angeles for more than a day or two you should already have one. The big point is this: The core of the Los Angeles transit network is the liberating high-frequency grid, which relies on the assumption that passengers can be asked to change buses once. Until now, the agency's policy of charging passengers extra to change buses was in direct conflict with the foundational principle of its network design.
Once more with feeling; Charging passengers extra for the inconvenience of connections is insane. It discourages exactly the customer behavior that efficient and liberating networks depend on. It undermines the whole notion of a transit network. It also gives customers a reason to object to network redesigns that deliver both greater efficiency and greater liberty, because by imposing a connection on their trip it has also raised their fare.
For that reason, actual businesses don't do it. When supposedly business minded bureaucrats tell us we should charge for connections, they are revealing that they have never stopped to think about the geometry of the transit product, but are just assuming it's like soap or restaurants. Tell them to think about airlines: Airfares that require a connection are frequently cheaper than nonstops. That's because the connection is something you endure for the sake of an efficient airline network, not an added service that you should pay extra for.
There was, for a while, an argument against free transfers that arose from the ease of abusing paper transfer slips. These slips, issued in return for a cash fare and to be presented on your second bus or train, were easy to give away or sell. Many US systems eliminated transfers and offered day passes instead, which improved security but at the high cost of discouraging spontaneous trips.
In any case, as soon as a transit agency has a working smartcard, there's no excuse for connection charges. They sometimes linger because managers and elected officials are desperate for revenue but are afraid to raise the base cash fare. In some cities, local journalists are too lazy to understand fare structures and just write quick scare stories whenever the base fare goes up. This motivates transit agencies to do desperate and devious-looking things to raise other charges, just as a simplistic obsession with low fares has caused airlines to invent endless fees.
But what matters is not just that the fare be low. It needs to be fair, and it needs to encourage people to use the system in more efficient ways. An efficient and liberating network requires connections, so penalizing connections is an attack on your network's efficiency.