Here is a partial list of books that will provide useful skills in the case we can no longer rely on a complex social order (where doctors, running water, and other modern day luxuries abound).
The Post-Petroleum Survival Guide and Cookbook by Albert Bates is a good starting place as it's light and witty and fun to read.
For a more serious account When Technology Fails: A Manual for Self-Reliance & Planetary Survival, by Matthew Stein is a good choice.
If you want to specialize, here are a few that'll get you started:
On basic survival and homesteading skills:
Tom Brown's Field Guide series is useful (on really roughing it)
as are The Foxfire Book series (on homesteading)
Also, if you want to learn basic medical skills, Where There Is No Doctor has proved useful in developing countries for decades now. Through the Hesperian Foundation, there are now over a dozen books of this nature: on dentistry, midwifery, is even one on Where There is No Dentist in case you're willing to learn to yank teeth without a license. All of these can be downloaded for free on Hesperian's website.
And if you do purchase any of these books (odds are they won't be in the library), remember to buy them used.