This New Haven, Conn.-based institution is hardly hurting for accolades. Three of the last four US presidents – Bill Clinton and both George Bushes – have been alumni of the school, and this year a mere 6.7 percent of students who vied for admissions to the school made the cut. But its QS stature has been backsliding in recent years. It was third in 2010 and fourth last year. Still, it’s got nine departments in the top 10 in their field, and an endowment second in size in the world only to Harvard, so the school is hardly down for the count.