If you are traveling internationally, this is a simple question. Yes! You need a passport for your little one, even if you are just going to Mexico or Canada. Many parents who haven’t traveled frequently may be unaware of the law changes in 2007 (requiring those entering the US by air to have a passport) and 2009 (requiring those traveling by land or sea to have one). Although there seem to be a few exceptions for children to enforcement of these laws, don’t risk it. A passport is your best and easiest chance to avoid detention at the border.
If you are traveling solo with your child (without the child’s other parent) on an international trip, you should also carry a signed and notarized note from your spouse authorizing you to take the child out of the country.
If you are traveling domestically, the answer to the ID question is a little more complicated. TSA will not require you to have an ID for your child at the security checkpoint, but an airline may ask for one in some circumstances. Southwest sometimes requires an ID for a traveling child (although I’ve never been asked to show one for my daughter on any Southwest flight yet). This is most often due to the fact that Southwest is one of the few airlines that still offers some child fares.
If you have an older lap infant, you should always carry an ID on any airline to show that the child is young enough (under the age of 2) to qualify as a lap infant.
In any of these circumstances, a simple copy of a birth certificate will suffice. So no need to rush to the DMV to get your tot a state-issued ID card! I always carry a birth certificate copy on any trip with my child — better to have it and not need it than need it and not have it.