Also, your chances improve of getting into an Ivey school if you apply to most of them
For most of the other Ivies, it also helps if you apply for "early decision" or "early action":
Early action - Wikipedia, the free encyclopedia
Early decision - Wikipedia, the free encyclopedia
If you were denied admission, my guess is that it would be just as well to reapply the following year since the Ivies don't mind a year off between high school and college if it is a fruitful experience.
Some statistics from the author of "A is for Admission":
Admission Statistics - Hernandez College Consulting
BTW, for perspective:
Who Needs Harvard?
Harvard Schmarvard: Getting Beyond the Ivy League to the College That is Best for You
And a new reason to consider Stanford:
Stanford drops tuition for some students