What I am going to say directly contradicts the advice many people give on ScubaBoard. I believe there are definite advantages to showing cards well beyond the most basic needed. I always show one of my most advanced cards, and it has many advantages.
The disadvantage people cite is their belief that the dive operation will stick them with a beginning diver in order to help that diver. This has not only never happened to me in all my years of diving, my experience has been the opposite. Dive operations almost always do their best to match divers by ability, not mismatch them. If you want to make it most likely you will be matched with the best divers, show your best card. If you want to be matched with their least experienced divers, show your least experienced card.
Here is an example to illustrate what I mean. I signed up for a dive the day before at the shop, and the shop owner took my information. I showed my instructor card, and we had a pleasant chat about my experiences as an instructor. The next day I showed up at the boat, and the DM set about finding me a buddy, since they did not allow solo diving. I noted that he did not ask one word about my experience, and I (stupidly) did not volunteer any information. I realized from the way he talked to me that he assumed I was a raw beginner, and I (stupidly) let him continue on that belief because I was peeved. He set me up with a father and son, who grudgingly accepted me as a buddy, despite the fact that they clearly resented having to deal with a beginner. When I saw they were setting up their gear incorrectly, I quietly helped them out, which obviously embarrassed them. At that point, the dive shop owner got on board, saw me, and came over to chat. He asked me who I was diving with, and when I showed him, his eyes grew wide with horror. He went across the boat, talked with some obviously very experienced divers, and I suddenly had new buddies.
Aside from getting matched with the most experienced divers on a trip, there are other advantages. You will get the benefit of the doubt during dives--DMs will let you wander more, and they won't be analy checking your gas pressure every few minutes. You get nice collegial chats with crew members. One time I even got a free dive. The boat was doing a specialty dive (sharks), and they needed a certain number of professionals in the water for their insurance. They were one pro short, and I became a crew member for the dive. All I had to do was go in the water first, direct the customers to the dive site (it was obvious), do the same dive I would have done otherwise, and then bring up the rear at the end of the dive. No problem.