The Cornell Library (print and online) or the web?
There are things freely available on the web that you won't find in the library. Many governmental, nongovernmental organizations (NGOs) and International Government Organizations (IGOs) post reports and sometimes data directly to the web. There are some amazing academic projects and important blogs.
There are also sources (journals and news sources) that post a few articles to the web, but then require payment for additional content. Google Books, of course, may have a preview (or sometimes the full book) of an ebook that the library doesn't have.
On the other hand, there's an enormous amount of material, not freely available on the web, that is only available through the print and online resources the library purchases -- books, ebooks, e-journals, data sources, news sources, government documents, primary source materials, streaming media, and more.
The library catalog and databases also offer ways to refine and filter your search that are not available in any web search engine.
Experienced researchers use both tools, and go back and forth between the two.
Follow the "next" link, below, to find out more.