I read a lot of books. Most of them are physical books, made from paper. I prefer to hold the books in my hand while reading. I do occasionally read books on-line though. Here is a list of, and a bit of commentary on, some online electronic book repositories.
The first site I'm going to mention is WOWIO. This site allows you to read some commercially available comic books/Graphic Novels online. This site was actually better a few months ago. Recently it started charging to download the E-books, in the past it would let you download three a day for free. Now you can read them for free online but they charge you to download them.
A site I used to hit fairly frequently is the Internet Public Library. If you go to the reading room on the site it lists several other sites to get free books. Personally I liked this site more several years ago than I do now. It was easier to find text on it then than it is now.
I have to mention Project Gutenberg since it is a large collection of books. One book on here that I particularly recommend is by Natsume, Soseki and it is called Botchan (Master Darling). This was written by a famous Japanese author and is very good. I own several of his other works. A few years ago the site had another of his works but it is no longer there.
Another site with many free texts is Blackmask now called Munsey's. On this site I had downloaded several of Robert E Howard's, creator of Conan the Barbarian, works. He is one of my favorite author's. I like his sword and sorcery with the Lovecraftian feel of his works. I particularly like that a lot of his works feature fictional pre-recorded history civilizations since I was always fascinated by early civilizations.
If you want books on religion, mythology, and folklore a good site to download them is Sacred Texts. This site has a lot of sacred books and mythology books. I like mythology, I find it to be very interesting.
Baen Free Library is a collection of books published by the company. They publish a lot of Science Fiction and Fantasy books. I read quite a bit of Science Fiction and Fantasy. The most interesting thing on the site, is the mention that by giving books out for free online, the sales of the actually copies of the books increased.
I am not really a fan of Doctor Who, I've seen only a few episodes of it at all, but I do know of a site that has quite a few free Dr Who E-books: Doctor Who the classic series.
There is also the Internet Archive which not only has a large number of books it has other media objects as well. Of all the sites listed, in this post, this website is probably the one I go to the most often though generally it is not for books. I go to the site for what it is known best as: a place where you can go to and read sites that are no longer being hosted where they were. I really dislike dead links and I find them far to often (it doesn't really help that I tend to look up older series such as Ranma 1/2 rather than newer stuff).
A couple more e-book sites are Many Books, which isn't working for me at the time of this posting, and the World Public Library Association which claims to be the biggest online repository of e-books, this site has a public section with around 75,000 free E-books and a member's section that has a lot but charges $8.95 a year. I don't really know much about these sites other than they exist.