The first thing you'll want to do before you head off searching for ebooks is to make sure you get the right ebook format for your ereader. If you're expecting to get a Kindle, look for books in Mobi format or, obviously, Kindle format. If you're getting one of the other ereaders, check the ebook formats it supports and select the appropriate format. Epub is a very popular format supported by most ereaders (except the Kindle, of course), so you may want to select this format if you're expecting a Nook or one of the other devices.
Now that you're armed with your ereader's preferred format, it's time to search for books. After all, you'll want to load books onto your ereader and begin reading immediately, right?
This being a site mostly dedicated to science fiction, I'll start with the Baen Free Library. Baen scores big over other publishers in their willingness to give away works by a wide range of authors. Not only do they give them away, they even allow you to give them away to friends, too. Baen supports a bunch of different formats, though it seemed to me they had fewer in Mobi/Kindle format than they did in epub format. That's not a disaster, as they also support various other formats, some of which will work on the Kindle and all of which can be converted to work on the Kindle (more on this later). Baen's Free Library is a great place to start building your ebook library while also picking up some very good works by some big name authors.
Baen also supports what they call a WebScription service, where you can purchase ebook versions of virtually everything Baen publishes. The prices are generally lower than the cost of a paperback, plus they have some really good deals on sets of books. (I've had my eye on a series of early books by Leigh Brackett, where the average price per book is about $3.)
Another obvious place to go looking for free ebooks is Project Gutenberg. Every book on this site is in the public domain, meaning it's entirely legal to download a copy of the book. The number of formats supported varies from title to title, but you can always find plain text, which is supported by every ereader on the market, and can usually find epub and Kindle format. I've pulled a lot of books off of Project Gutenberg, including a lot of early science fiction (find it grouped together here), mysteries, folk and fairy tales, and historical books.
Watkinson provided a link to eBooks@Adelaide, another place to find books in the public domain. I suspect titles on this site has a fairly large cross-over with titles on Project Gutenberg, but the books may be better edited (being associated with a university rather than being a volunteer-support project like Gutenberg). The only supported format here is epub, but that isn't a barrier to reading the books even on the non-epub-supporting Kindle. To download one of these books, click on the green, stylized 'e' for epub. Otherwise you'll have to read the book in your web browser.
The web is also full of sites at which authors may electronically publish their works, either offering them for free or selling them. Our very own M has stuff on Smashwords (and if you ask nicely, he might even electronically autograph his work). You'll have to create a username to access the books, but it's free and Smashwords doesn't hit you with any spam (I've had a username for months and they've left me alone). God only knows how many similar sites there are online.
Two other very good places to look for free ebooks are amazon.com and barnesandnoble.com. Both sites have thousands upon thousands of free titles. I've heard that many of the ones on amazon are simply titles amazon has "harvested" from Project Gutenberg and is making available at the same price. I wouldn't be surprised to learn that Barnes and Noble has done the same thing. One advantage to download these versions rather than the ones from Project Gutenberg is that the store will have already formatted the book for your ereader (assuming you have a Kindle or Nook).
For those who haven't seen the news, Google is apparently about to dive into the ebook market, too. I assume they've gotten over their previous "we get to make your book available for everyone to download unless you specifically tell us otherwise" stupidity, but you never know when it comes to Google. (Why everyone bitches about Microsoft when you've got "Do
Finally, let me mention Cory Doctorow. Cory makes every single one of his books available free for download from his website. Further more, he makes the available at the same time they are being released new in hardback. Most of the formats are supported. You will probably have to right click on the file type (AZW is the file format for Kindle, btw) and select "Save Link as..." to download a book. I mention Cory's site because I find his approach interesting and suspect he's doing quite well with it. If you like what you read, you're welcome to donate to the cause (thereby skipping the publisher and putting money directly in Cory's pocket). Or you can just keep the books, pass them to your friends, etc. Cory very specifically grants that right for each of his books.
Now, I've talked a bunch about files and where to get them. I've also mentioned converting them. This is where you learn how to do that. I stumbled across Calibre ebook management software the same day I got my Kindle. In my Kindle review, I told you that Calibre will convert ebooks from one supported file format to another supported file format (and it seems to support all of them). The software also provides an easy method of managing the books on your ereader. I know all of the ereaders already have software that will handle file management, but Calibre has the advantage of both handling file conversions and managing the books on your ereader. Calibre supports all of the major devices, automatically detecting them when they're connected. I didn't have to tell Calibre that I had a Kindle, it simply picked up the type of device connected and away I went. The software is also very easy to use but has extensive help files should you find yourself in need of assistance.
This ought to be more than enough to get all of you prospective ereader owners started. You've got five days until Christmas. With only minimal effort, you can have hundreds of titles ready to load once you've got your new toy.