I've known my SSN since I was 16, when I had to fill out like a bazillion job applications to find a part-time job. I have a retail job for the summer now, and some lady AT LEAST as old as me (probably older, maybe 22 or 23) didn't know hers. She wanted to sign up for a credit card for our store, so she had to call her brother at home to get him to dig through her wallet until he found her social security card (which is the LAST thing you want in your wallet, in the first place).
It worked out in the end, but it took her like 15 minutes. Really, by the time you're out of high school there is no reason for you to NOT know your SSN. You're an adult, and as an American it's about the most important number you can know.