Speaking from a profession dominated by credential whores I can tell you its pretty important. We do 50% of our hiring from Ivies, 40% of our hiring from the Harvard's of the Midwest, West Coast and South (Michigan, Duke, VA, Berkeley, Stanford, NYU, et al). The final 10% comes from the remainder of the schools.

When it comes to top top jobs, i.e., Supreme Court Clerkship, if its not one the aforementioned schools, don't bother applying. I had the benefit of both worlds, Michigan undergrad, Columbia Law School. I wouldn't change either choice.