It depends on the ebook reader you've got. Some will restrict which sites you can download books from; eg, Amazon's Kindle will only generally allow you to download books from Amazon. Most will have restrictions on what ebook formats they'll work with.
You can get absolutely free ebooks in a variety of formats from Project Gutenburg. These are mainly books out of copyright so lots of classics, not much contemporary fiction, but you may be surprised. They do have an incredible range of stuff.
You could also try ebooks.com for contemporary fiction and a lot of other stuff. You'll need to stump up for this but it's generally cheaper than paper.
Again, though, before buying any ebooks, do double-check to make sure it's compatible with your reader. They're not nearly as standardised as they could should be.