Your school should help you out. It varies greatly between states, so you need to sit down with an advisor at your school and ask. A big thing that can keep you out across the board is a recent bankruptcy. Lawyers are expected to be fiduciaries, and handle client money, property, and financial transactions. A lot of bar committees reason "if a lawyer can't keep his or her own financial house in order, then how can we expect them to be trusted with money by a client?" I know bankruptcy isn't always like that, and for most people it involves circumstances totally outside of their control, but that's how the bar committee thinks.
The best rule of thumb in applying to the bar is when in doubt, disclose it. The vast majority of bar applications that are turned down or significantly delayed are the result of concealing information which would not have kept you out in the first place.
I think some states might have an interview, and my bet is all would have an interview or hearing in the case of a problem with your application. I'm not sure about an interview as part of the normal process though.