A-ticket would allow you to ride tamer rides like King Arthur's Carousel.
Tickets were distributed by various ticket booths throughout the park. At these booths, guests could purchase either a ticket book, complete with A, B, C, D, and E-tickets; or individual ride tickets. Today, these ticket booths can still be found in Disneyland, but they no longer sell tickets.
As you can see, three of these ticket booths are just decorations - only one still functions as a kiosk, providing film and photo information. The mushroom ticket booth in front of Alice and Wonderland seems to have had either its window sealed up, or been replaced entirely. If you go around towards the back of the mushroom there's a door (the corner is just visible in the picture above), hinting that this may perhaps be the original ticket booth. The lighthouse ticket booth, however, appears to be just a replica. I've looked at old photographs of the original ticket booth in front of the Storybook Land Canal Boats, and the position and size of the lighthouse seem to have changed. To my knowledge, at least a couple more disguised ticket booths can still be seen at Disneyland. They won't be easy to find, but it makes for a challenging hunt. Nevertheless, it was a thoughtful decision to leave the ticket booths be, to remind guests of the era of A-tickets and E-tickets.