In college many years ago our STUDENT ID was our SS#! Grades were dutifully posted on hallway bulletin boards (the cork, non virtual kind) with the grade by our social! Times HAVE changed!
When I first got a DL your SS# was your license #. The state made it easy to change a few years later.
I remember that too!
Also, there was a time when the military used your SSN as your Service Number
EDIT - I thought they stopped that but searching indicates the SSN is your Service Number.
The military definitely stopped using SS numbers for military IDs. If your ID predates when they stopped, it probably still uses your SS number, but the ne t time you get a new card, it would change.