My knowledge comes more from science-ish departments so my advice falls in that vein. I know nothing of, say, humanities grad schools. Granted the following 2 examples should be fairly generalizable.
One very typical question could involve "why this school or program in particular?"
They want to hear something about them that makes you a good fit. If you say, well you guys are very well ranked and thats it you'll come across as a less desirable candidate that someone who says "you guys are very well ranked and I like the way the program is set up because of xxxx interdisciplinary aspect and the research many of your professors do such as xxxxxxxx is particularly interesting to me.
another question that often comes up is, "tell me about yourself." You'd best talk about your academic interests and how you got yourself involved in your current major(s) and any related experience you might have. Also, explain what you hope to get out of grad school.
Best of luck!