Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, Princeton University, the University of Pennsylvania, and Yale University all have extremely high expectations and cost more than most Americans can afford. They select students based on a lot more than just grades.
Most of the people I know that go were born with a silver spoon, but money isn't enough. They look at things like civic participation, after school activities, charity work, etc.
I'd say that most are typically over achievers. I've always considered it fairly close to what you'd find at Cambridge but I haven't visited that campus so I don't know for sure.