In Illinois, your date of birth is actually encoded into the last 5 digits of your drivers license number. "Encoded" is probably being too generous - it takes very little effort to decode, and there are decode instructions on the Internet.
Ditto on what the others said. No state just puts that sort of information out on the Internet. On the other hand, those Web sites that offer to give you someone's life story for $49.95 can probably get more info about you than you want to know with a DL number.