Google Books - the project to digitize several major research libraries' collections - includes magazines as well. Starting today you can browse all of the weekly issues of Life from 1936 to 1972 (over 1,860 issues). You can read more about it here.
Browse issues of Life here.
One of the nice things about this is that it supplements our digitized edition of Life through InfoTrac Academic OneFile, which indexes the title from January 1, 1965 to May1, 2000, and has full-text available from January 2, 1965 to May 1, 2000. The InfoTrac version is in html and does not include photos, whereas the weekly issues scanned for Google Books are fully digital copies of the original. You can also search photos from Life using Google Image search. Hint: search specifically for Life photos in Google Images by searching for keyword source:life.