As soon as the new cards arrived I went to FedEx/Kinkos and had them laminate the cards. Its sort of ironic that the change was made to protect the secrecy of our Social Security Administration numbers, even though the original cards clearly said they were not to be used for identification. When I entered the military in 1966 we were issued "Service numbers". Three years later, in 1969, everyone's Social Security number became their new Service Number. All of my dependents' ID cards used my Social Security number to identify them and verify that they were legitimate dependents and eligible for military benefits. Then all of a sudden, in the internet age, Social Security numbers became something not to be shared because the credit agencies were using them to verify identities. Weird. But it is likely that all sorts of people already know your Social Security number, particularly any organization that is billing your insurance company or the government for health insurance purposes.
Just think, every clerk that processes any document relating to your health care has access to your name, date of birth, Social Security number, address and other data with which to "steal" your identity.
A number of years ago, due to just this concern over identity theft, I instituted a "security freeze" for myself and my wife with the three national credit agencies. At the time it cost me a total of $60 to get this done, but in my opinion it was well worth it. We have never had an issue with identity theft, and whenever I have needed a credit check to be done I just call in for a temporary lifting of the freeze, a simple no cost process.
So even with your new SS card, don't be careless about identity theft. I think the "security freeze" plan is just as effective, if not more so, than paying every month for something like "LifeLock". FWIW, one of my son's, who used to be an identity theft investigator for the State of Wisconsin, said that LifeLock and other's like it were basically worthless and a scam.