No Steve! However, many states issue Photo ID Driver's licenses. Also, many credit cards now include photos. The latter are optional, given on request. Some sates even issue special driver's licenses that verify that you are a US citizen. This is useful in states that border Canada as you can then cross the border without a passport.
Spot on PE. States DO issue photo IDs in lieu of driver licenses for those who don't drive, and anyone here who can't or doesn't drive would be nuts not to get one as there are so many things you must have one for (including buying alcohol or getting into many places that serve it, often even if you are clearly as old as Methuselah) but you certainly aren't legally required to get it, much less carry it.