A lot of people are interested in getting ebooks from their local libraries. That is clear just by reading the comments on this website, as well as from the big news that the Kindle now supports library ebooks.
Many people who own e-readers might be interested in this, but not know where to begin. I found this video at PCWorld that walks you through checking out an ebook from the Boston Public Library:
Obviously you will need to check with your own local library, but as far as I know most of them use the same system provided by Overdrive, so the process at your library will probably be very similar.
This was already possible on e-readers like the Sony Reader, but it was a feature that the Kindle lacked until very recently. There is more information in this blog post from ZDNet.