Well, I went to Brown and majored in philosophy; I can say the following: (1) I think I got an excellent education, and (2) being able to write 'Brown' on resumes and applications seems to have given me an advantage in certain situations.
It certainly made it much easier for me to get a paying gig as a summer associate after 1L year of law school (without any law school grades to look at, firms heavily consider your undergraduate school and record). I go to a top-ranked non-Ivy law school, but it seems like people I meet, including lawyers, are more impressed with my undergrad school.
There are plenty of great schools, Ivy and non-Ivy, but all-in-all, the Ivy League represents some of the best colleges in the country. I don't think that's a particularly controversial claim. They are extremely hard to get into, so it makes sense that they would have academically more successful students. Are academics everything in life? Not nearly. But pretending that getting into a top undergrad means nothing is ridiculous.
Another thing to consider: for better or worse, the Ivies are strongly insulated from shifts in rankings. It's nice to have that kind of value retention behind your degree.