I've always preferred the look of calling cards over business cards. Here are some I had made. They are more pleasant than your typical business card, and they come packaged like a gift.
Most calling cards are printed on both sides, and on think paper, and they are often decorated very artistically. They feel like a small piece of art rather than a business card.
The company I bought these from told me that calling cards are often popular with two groups of people I had not considered: Stay at home parents who meet other parents at the play ground, and dog owners who meet other dog owners at dog parks.
I like giving them out as business cards, since they look nice and other people often comment on them when receiving them.
For more information on calling cards, see this great article recommended by David Dickens titled The Gentleman’s Guide to the Calling Card - http://artofmanliness.com/2008/09/07/the-gentlemans-guide-to-the-calling-card/ It talks about how to design and use calling cards, and where to have them made.