Business cards are most often basic. Sometimes they are attempts to be innovative in a way that can make eyes roll.
The website [Re]Encoded, however, has a fantastic gallery of card designs that are innovative and not the least bit cheesy: A landscape team prints its phone number on seed packets. A post-marriage counselor's card is ripped and taped back together. A chest physician's "cards" are printed on balloons.
It's creativity done right.