A few of my fellow students bought themselves official university-approved business cards a year or so ago, and have been happily handing them out at conferences and when sending out papers to colleagues. At their recommendation, and with assurances as to the speed with which the office could print off the cards, I followed their example. Unfortunately, the office was going through a slow period, and by the time the cards were ready, several weeks later, the conferences I was attending during the fall semester were over.
I hadn't thought there being anything wrong with the idea of having business cards until I discussed them with a postdoc student in my department last week. He laughed at the very concept of having business cards before being ensconced in a long-term position of the sort where the employer provides the cards. Such as a faculty position. Graduate degrees are professional degrees, however, and can be quite time consuming. Are law students expected to have business cards? Are business school students?
I'm under the impression that for humanities graduate students, it's not common, but neither is it unheard of. Two students I met through last year's Vagantes conference have business cards, subsidized by their department.