Some things to bear in mind:
- There is no giant Amazon-equivalent that hosts all the DRM-free e-books in the world; instead it's a lot of little stores.
- Not every e-book has a DRM-free edition, so if you're looking for a specific title you might not find it. :(
- Different e-readers use different file formats, but DRM-free e-books can be converted between them with the free Calibre software. If a vendor only sells .epubs and what you've got is a Kindle (which reads .mobi), you're still cool: you can buy the .epub and convert it to .mobi with Calibre.
- Some of these stores may be based in a different country than you. Many use Paypal to address this issue; even if you don't have a Paypal account, you can pay with your credit card through the Paypal interface.
Project Gutenberg: All DRM-free. These books are free. Project Gutenberg collects, digitizes, and distributes public domain works. If it was published before 1923, it's probably here. (Project Gutenberg is based in the United States: copyright law may be different in other countries.)
Calibre Open Books: All DRM-free. This source is an attempt at indexing as many DRM-free works as possible. It's not everything, but it's extensive. This is a catalog, not a vendor: the links that say "Download" do not actually download the book - they lead you to the website where you can buy it.
AllRomance Ebooks: Sells both DRMed and DRM-free books. The DRMed formats are labeled "Secure" [I think]; more information on formats at their FAQ. Independent e-book store, multiple publishers. Sells multiple formats; re-download available only in the format you bought it (and possibly not available for DRMed ebooks). Prices in dollars.
Angry Robot: All DRM-free. Publisher storefront for Angry Robots. Sells .epubs only, which you can convert with Calibre. Re-download of purchased books available. Prices in pounds.
Baen Ebooks: All DRM-free. Publisher storefront for Baen Books, plus a smaller quantity of titles from about a dozen other publishers too. Sells multiple formats; re-download of purchased books in another format is available. Prices in dollars.
Diesel eBooks: Sells both DRMed and DRM-free books. The DRM status of each book is clearly labeled in the book details. Independent e-book store, multiple publishers. Sells .epubs only [I think; you can convert with Calibre. I haven't bought here yet, so I don't know if re-download is available.] Prices in dollars.
Rebellion: All DRM-free (I think - I can't find a FAQ or anything explicitly stating their position on DRM). Publisher storefront for Solaris and Abaddon. Sells .epub and .mobi (you can convert with Calibre). [I haven't bought here yet, so I don't know if re-download is available.] Prices in pounds.
Smashwords: All DRM-free. Indie publishing; a major source for self-published works. (Mostly by people you haven't heard of, but traditionally-published authors also sometimes sell their backlists or experiment in self-publishing here.) Sells multiple formats; re-download of purchased books in another format is available. Prices in dollars.
Weightless Books: All DRM-free. Independent e-book store, multiple publishers. Sells multiple formats; [I haven't bought here yet, so I don't know if re-download is available.] Prices in dollars.
Wizard's Tower: All DRM-free. Publisher storefront for Wizard's Tower Press. [Although I think it also hosts items from some other small presses too?] Sells .epubs and .mobis (you can convert with Calibre); re-download available. Prices in pounds.