Technically, you can still use them to this day to reduce the cost of admission.
EDIT: Just saw your signature so I'll add that Adventure Thru Inner Space didn't require a ticket for much of its life due to being sponsored by Monsanto (and a lot of people called it "Monsanto," as in "Let's ride Monsanto").
And to note, the tickets were not there at opening. They came along a little later in the year as an easier way of paying for attractions and started with only the A-C tickets. The D ticket was introduced in 1956 and the E ticket in 1959. And while popularly known as "tickets," the tickets themselves are labels as a "coupon."