Should indexing be fair use? The battle over Google Book Search

In late 2004, Google announced as part of its Library Project that it would scan millions of books into a searchable online database accessible to anyone using Google Book Search (http://books.google.com). In response, the US Authors Guild and the Association of American Publishers (AAP) sued Google, claiming its book scanning is "massive copyright infringement". Google says its indexing is a legitimate fair use. As in all such discussions, two different questions arise: What does the law say? What would be good public policy?