Excellent question. The very best universities don't intermingle them... MIT, Caltech, Stanford come to mind. I know MIT has lots of intramural sports, where the focus is on healthy recreation for students. But they don't have ANY NCAA-style teams.
Stanford has one of the country's biggest and most successful NCAA Division 1 athletics programs.
"Stanford has won the NACDA Director's Cup for Division I, awarded annually to the college or university with the most success in collegiate athletics, for 14 consecutive years (1994-95 to 2007-08)."
I'm not really sure as to what you mean by NCAA-style teams. Stanford is actually the school that the sports world points to as the shinning example of excellence in sports not interfering with excellence in academics. In fact last year Stanford Basketball went to the sweet 16 in the NCAA tournament. Before his career as pro-quarterback John Elway was a Stanford student-athlete. Furthermore every university in the academically vaulted Ivy league is also a member of the NCAA Division I.
Tell you what, though: when I chose between Stanford with its athletic program and Caltech with its lack thereof, I considered the athletics a knock against Stanford. I ultimately chose Stanford, but despite the athletics, not because of them.
This is just not true. MIT competes in Division III and has 41 varsity teams according to wikipedia. I'm not sure if they give out any athletic scholarships.
