Jim Lynch of ExtremeTech ran a nice how-to article about getting free ebooks on your Amazon Kindle. If you're Kindle-enabled, it's worth a read, but even if you have a competing e-reader, or just read ebooks on your computer, there's some good info there too, because Mr. Lynch lists five sources of free ebooks. Number five is the Kindle store itself, so won't be of use to the rest of us, but of the other four, two are for tech books and two are more general interest.
But of course there're more ways to get free reading material for your e-reader, and I thought it might be worth mentioning a few. See the last page of Mr. Lynch's article for tips on getting them onto your Kindle; I'm going to be platform agnostic.
There are a few big sites that are the source of a lot of public domain ebooks. Lynch mentions Google Books but there is also Project Gutenberg (which also offers some titles in audio format) and Wikisource. It's worth noting that once you've found a book you like on the latter site, click the "PDF Version" link under the Toolbox menu in order to generate a PDF to download. Otherwise Wikisource allows reading directly from the website.
FeedBooks.com takes content from the above public domain repositories and wraps a more full-featured website around them. You can download the books, of course, but they also provide some social services between users of the site, "similar book" features and that sort of thing. It is, in my opinion, a more user-friendly site than the main repositories themselves.
I'm a fan of science fiction and fantasy, so one of my favorite sites is the Baen Free Library. It's not very flashy, and of course they only list Baen books, but there's plenty of free genre fiction to be found there. Not to be outdone, Random House fired back with its own ebook library, Suvudu, that has a free ebook section as well.
For content you can't find anywhere else, there's Wikibooks which bills itself as a "community for creating a free library of educational textbooks." I just now discovered this one but it seems to cover a wide range of topics, from cooking to programming!
So that should get you started, but I know I've missed some gems (particularly in genres I don't really follow); the internet is a big place! If you have a favorite source of free ebooks, please leave a comment and share!
Oh, and I mentioned that Project Gutenberg has some titles as free audio books. If audio books are your thing, check out PodioBooks.com. This site will podcast an audio book to you, a chapter at a time (at a frequency you determine). The books are free but donations are encouraged. I've used the service a lot and it's pretty amazing. And no, I'm not affiliated with it or any of the other sites listed here today. I'm just a fan.