If you are traveling with an infant, it is imperative that you tell the airline at the time of booking. A ticket is required for the infant if traveling internationally. This is usually at a percentage cost of the adult fare. Usually, if traveling in your own country a ticket is not required. A boarding pass may be required in order to clear security though.
Also, on certain airplanes, you have to sit in specific rows due to the number of oxygen masks available in that row.