It is almost impossible to imagine life without a cellphone. But imagining life without a cellphone bill is getting a lot easier.

For 30 days beginning in January, I disconnected my iPhone from AT&T Inc. and lived entirely off the free Wi-Fi connections that are available nearly everywhere. It wasn’t exactly seamless. An effort to dump extra tickets to the NCAA College Football Championship game in Dallas was more stressful than it would have been with an always-connected phone. On occasion I had to lean on friends who were...