How important is it to have done a banking internship?

In this job market, an internship is almost mandatory.  Having done an internship in banking (either over the summer or during the school year) shows (a) that you are serious about banking and (b) that you have a good idea of what you are getting into.  Being able to demonstrate both A and B because of an internship will go along way in helping you differentiate yourself during the interview process.

For MBA students (who were not Analysts pre-business school), a summer banking internship is extremely important when it comes time for full-time recruiting.  Interviewers will tend to question how serious is your interest in banking if you did your internship in another industry.