What did formals for the Army, Marines and Navy look like back in 1960?

In the late 60s - early 70s, all I can remember of formals was the annual Marine Corps Birthday Ball - I went to my first one while on MSG duty in Ottawa. Of course, we Marines all wore the Blue "A" uniform. While there, I also attended (with my SNCOIC) a formal New Year's Day levee (reception) hosted by the Governor General of Canada - it was fun, because all military personnel were in full dress (what the Canadians called Levee Dress) in distinctive regimental uniforms. We wore our Blue "A" uniforms, and I believe we were the only enlisted personnel there. All the officers in line had engraved calling cards to hand to the Governor General's ADC so he could announce them. Needless to say, my MGySgt and I (a sergeant) felt a little under-gunned by this situation since we had no cards, but the Canadians had anticipated this possibility and positioned a small table with 3x5 cards and pencils just beside the receiving line. So the MGySgt and I quickly made "calling cards" and handed them to the ADC as if it were the most natural thing in the world, got introduced to the Governor General, and then went into the bar, where things were less formal. It was a good time.
As to other formal occasions, I believe the officers had mess nights (stag) and dinings-in (with wives). Later, when I advanced to SSgt, I was able to attend SNCO mess nights at various posts, and the annual Marine Corps Ball. The degree of formality was that those who had dress blues or evening dress uniforms wore them, and everybody else wore the Service "A" uniform. I don't know if they would count as formals, but I also participated in a couple of full-dress parades at which we wore the Blue "A" or the Blue-White "A" uniform with white gloves, swords, medals, etc. Actually, I think parades should count as "formal" due to the discipline, music and precision movement experienced by all participants.

umm... Do you mean balls/dining in/dining outs???

Don't know about the 60's but went to few Army formals in the 70's. I remember the Mess Dress uniforms that the senior officers wore with all the extra braid on the shoulders and even dress white uniforms-I had a set of those myself. There was of course the giant Punchbowl and lots of toasts with some concoction composed of various liquors and wines from our nations military history. Good place to meet people, learn a few things, and hear some good war stories.