I know for really little babies you don't have to pay, but I'm not sure if they just give the seat to a baby or if the mom has to carry it on her lap.
I did see a program on TV and some flight attendants were really squaking about how dangerous it is to have an unrestrained baby, especially if the plane hits bad turbulence. If the plane hits an air pocket and drops suddenly all the people hit the ceiling, imagine what that would do to a baby. They were trying to get the legislation changed...but I don't know if it ever happened.