I'm curious.... What schools have cutoffs? What are they?
I think the average board score question is really hard to answer. There was a thread here not long ago titled something like "for those of you who matched" which had people's board score and where they matched. I can't seem to find it anymore, but maybe we can repeat it for the folks who will be applying in September.
I think it's safe to say the average board score will get you into a good program, while an above average score will get you into a very good to excellent program. But the programs also tend to look at the complete picture (grades, research, personal statement, letters, experience, etc.), too.