Nathan over at the eBook Reader Blog writes:
Amazon and OverDrive have quietly started rolling out Kindle ebook lending from public libraries, albeit in Beta. Even though there hasn't been any official announcement yet, some public libraries have already started lending ebooks for the Kindle...Plus the Device Resource Center over at OverDrive now lists the Amazon Kindle 3, Kindle DX, Kindle 1, and Kindle 2 as supported devices. The library ebooks will also work with Kindle apps and the Kindle Cloud Reader according to the public library books help page at Amazon.
Other e-readers, such as the Barnes&Noble Nook and Sony Readers, have offered the library lending feature for a while and some users swear by it. Basically, if your local public library offers e-book lending (and you have a library card) you can check out an e-book for a set period of time (usually less than two weeks). Often, there's a wait list for more-popular titles--and only a fraction of e-book titles are available for borrowing--but the best thing about the service is that it's free.