In order to maybe cut down on some of the lackluster answers, I'll put in a few clarifying questions on what the original question (I presume!) is asking:

1. When did a driver's license first become a valid form of identification in the US? Did it replace an older form of state issued ID?
2. When did stores in American first have to ask for a form of identification to sell everyday age-controlled items like cigarettes and alcohol? (This is the most common reason to need a form of driver's license/state ID on you at all times)
3. When did common government and non-government services start requiring an ID to access, such as setting up a bank account, voting, or getting a library card?