There is an important difference between the ebooks you can get off of websites and the ebooks the library offers. The ebooks the library offers come with check out periods, so after a set period of time the books will be removed from your device unless it is an ebook with unlimited downloading capablity and no checkout periods.
On the internet, fiscally speaking, there are two types of ebooks you can download: paid and free. The paid ebooks are typically books still under copyright available in an ebook format. This would include most new fiction ebooks. If you have a Kindle you can buy ebooks from Amazon.com. If you have a NOOK you can buy ebooks from www.bn.com. Sony eReader you can buy from their reader store.
However, there are many sites such as Project Gutenberg that offer free ebooks for you to download to your device for as long as you would like. Most of these books are older materials that are no longer in copyright or works that authors and publishers have decided to offer for free. Some of the sites that offer free downloads are shown in the box to the right.
Here are some free sites on the internet that provide downloadable ebooks.