I went to my local, public library the other day. You might ask why a Google guy would visit the archive of ink-on-crushed-trees, and the answers are pretty simple: I go for two key reasons -- (1) Because they have things I can't get otherwise and (2) because they have reference librarians.
In the category of things-I-can't-get, here's the list of things I picked up: 3 CDs of chamber music (Mozart, Shostakovich and Hindemith), a set of lectures on CD with notes (on the topic of Chamber Music), and two books of limericks.
Yes, I could have bought all these things through Amazon or equivalent online--but it would have been well over $200.
Through my public library I also have access to a set of databases that are invisible to Google--they don't license their data or access to their data, so there's no easy way to get that kind of information without going through the library. There are great genealogical resources there, as well as full-access to all of the New York times going back to 1851. Want to read the story of Fordlandia (the ill-fated city-of-rubber than Henry Ford built in Brazil in the late 1920's)? Read the original coverage in the Times. It's $3.95/article if you don't use your public library.
And, lastly, reference librarians are both incredibly well-informed about the infoverse AND incredibly happy to tell you everything they know in order to make you a better researcher. I like that. I like it a lot--they're not out to make a dime from every transaction, but they're genuine saints who want nothing more than to teach you how to do the search on your own and make you self-sufficient. You have to admire that in these days of unrelenting grabs for every last surcharge for expertise.
I have many reasons to use my local library--but perhaps the best is that it's a place where I always learn something. (The last time I took a class on Search at the library, I found out that you can use the * within the scope of double quotes--a la [ "Obama said * about Israel" ], which will find all instances of that phrase with something matching the asterisk. While it makes sense (the double-quotes prevent synonyms from triggering), I didn't think the asterisk would function correctly within the quotes! It's a place where I can see the latest books, magazines, music, video and all the regional news.
It's my local library--and yes, I still go there, even as a Googler, about once a week...
Search on! (Even in the stacks!)