To be honest, it is really dependent on two factors: how strong your application is and how much you actually need financial aid. I am currently at UPenn (need-aware for international students) and chose not to apply for financial aid because I believed it would affect my chances of admission, but I do know many other international students (including other Australians and New Zealanders) who have received financial aid. In the end, if the school sees you as someone who offers something significant to their community then they will be “generous”.

Though applying for financial aid does affect your Admissions chances, most Ivy League schools are in a similar realm (along with other top ranked private and liberal arts colleges) in that they have large endowments and fairly strong financial aid.

Need blind Ivy’s (Harvard Yale and Princeton) are the most generous but beyond that they are all generous to strong candidates, exactly as Nathan said.