There is usually no problem with wearing "Class Rings". The same goes for Wedding Bands. If, however, you want to dress up like a NY Pimp, well then someone will have a talk with you, and it will not be profitable.
In most cases, it is advisable not to wear rings, or any jewellery, as it tends to get caught in machinery or weapons and especially in the case of a ring, could cause a rather unpleasant and painful amputation with no medical assistance nearby.
A friend of mine, on scaling a fence, brought that home to me. When coming down, his ring caught and his body weight nearly amputated his finger. In the hospital, the doctor gave him the choice; save the ring or save the finger. After three tries, he decided the ring wasn't all that important, and the doctor cut the ring out.
I'll end with "save the cheerleader - save the world!"