I'm planning on applying to a couple of Ivy League schools. I know that they vary a bit in their expectations, but what's an estimate of how many AP classes should I take in high school if I hope to attend an elite college?
Students who attend schools with a reasonable number of AP offerings are often expected to take around 7 to 12 classes total. There's no one standard recommendation I can give because the number of AP classes available at each school varies dramatically. If your high school offers only 8 APs, for example, taking 7 of them would be more than acceptable.
You can even get into top schools without taking any AP classes at all if you don't have access to them. Elite colleges will not reject students just because they attended a high school with few or nonexistent AP offerings. If you do all you can to challenge yourself within the constraints of your environment, you will have a chance regardless of how many AP classes are on your transcript.
If your school doesn't offer AP classes, you might think about self-studying for an AP test and/or taking local community college classes to show that you're up for an academic challenge. Some schools offer IB classes, which are another set of advanced courses that are considered to be on par with APs. You don't have anything to worry about if you take them instead, though you may have a harder time earning college credits for your test scores in some cases. For more detailed advice on AP classes and Ivy League admissions, read this article.