I had a set of cards made, and I definitely feel that they help while requesting permission on private property, or for establishing a network of potential permissions.
When door knocking/cold-calling, I think it creates a certain level of credibility to what otherwise is a pretty odd request - we are asking someone to allow a complete stranger to dig little holes all over their lawn, after all
Plus, I think it also helps to generate some trust: I have my home address on my card in addition to my other contact info - in my mind, if I know where they live, they should know where I live. Along the same vein as trust, I splurged and had double sided cards printed, using the back to list my version of "the code of ethics". It serves as a reminder that I intend to fully respect their property.
But the greater value of cards may well be for building up a network of potential permissions. How many times have you been out detecting, and someone asks, "found anything good yet?" In most cases, I'll engage that person in conversation for a little while, and they'll most likely walk away with one of my cards in hand. I want to make sure that if they really are interested in finding out what might be hiding in their yard or if they ever lose something, they remember me, and I'm the one they call
Heck, if you knock on a door to get permission and the landowner says "no" had him a card and say "here's my card just in case you lose something of value or you change your mind". The way I see it is even if he or she doesn't lose anything of value, they might know someone that has or will in the future.
+1 on this! One of the huge benefits of having a card to give out! Without a card, a "no" is (somewhat) permanent once they close the door. If they change their mind, or lose something, they have no way to contact you. But left with a card, I'm likely the first person they'll think of, and I can be readily reached.
Sure, the vast majority of my cards will end up either thrown away or in the bottom of someone's junk drawer. But if only a couple of those cards results in a new, unsolicited permission, then they easily paid for themselves!