Harvard is probably the school most synonymous with the Ivy League, and its prestigious reputation is well-deserved. Students enjoy access to the largest university library in the world as well as some of the most illustrious faculty members, including Nobel Prize-winning economist Alvin Roth and cognitive psychologist Steven Pinker. Harvard alumni are well-represented at the top of most professions, ranging from music (cellist Yo-Yo Ma) to politics (former President Barack Obama) to law (Supreme Court Chief Justice John Roberts).

If you get in, Harvard can also be surprisingly affordable. The schools says that families earning less than $85,000 a year (which includes more than 20% of Harvard families) won’t have to pay anything for their college student’s education. If their annual income is between $85,000 and $150,000, they’ll only be asked to contribute 10% at the most, the school says.

It pays off: Most students graduate debt-free, and the median earnings a decade after enrolling is around $95,000. Harvard has one of the nation's highest graduation rates, at 97%.

The university fields 42 Division I sports teams that have won more than 150 championships in total. The campus gears up for football and tailgating at the much-ballyhooed annual game against rival Yale.

Another fun aspect of Harvard life is its residential system. On Housing Day each spring, costumed upperclassmen storm the freshmen dorms with gongs and other props to tell students of their randomly assigned placements into one of the school's 12 houses — one of which features a guinea pig room.