I'm actually surprised to see so much love for Illustrator in response to this question, but all the business cards I've done have been very sober corporate designs, so I guess the drawing tools weren't necessary. Our shop used InDesign exclusively for business cards, and wouldn't have dreamed of using IL or PS.
ETA of course I should note that a company logo would be done in IL or PS, but that's because the logo would be used in multiple jobs, and so would always be artwork created outside InDesign.