In the book Yours, Isaac Asimov, a small percentage of his letters are collected together, divided by theme. The first theme is, of course, letters, and editor Stanley Asimov shares a few of the letters that Asimov wrote mentioning the fact that Boston University wanted to collect all his papers - not only his books but also his rough drafts, his letters, and any scraps of paper.
It wasn't strictly just for him... the University wanted to establish archives of all prominent authors who had attended the school or who had worked there.
West Virginia Libraries has a site dedicated to him: http://www.libraries.wvu.edu/exhibits/asimov/
here's what's in the Boston Archives.
Or go here and do a search on Isaac Asimov: