I discovered free online books some years ago...my favorite site is http://digital.library.upenn.edu/books/
. I used to recommend DailyLit.com as a way to read longer classics slowly (they email you a page or so every day) but they have had a lot more technical problems since they were bought out a couple of years ago.
In terms of specific books that have held up well over time for me:
Huckleberry Finn (Mark Twain) really moved me as an adult when I was old enough to understand the historical context in which Twain was writing, and why saying that a white boy and a black man could be friends was so subversive.
Jane Austen is still a great read if you like novels with vivid characters and great conversation. I also really liked Elizabeth Gaskell's books (similar genre, slightly later period) North and South, Cranford, and Wives and Daughters which I found through the BBC adaptations.
Sherlock Holmes is still fun although I did notice when I read the Complete Works recently that I was figuring out the mysteries a lot quicker than when I was a teenager.
The early books of L.M. Montgomery (Anne of Green Gables), Agatha Christie, and P.G. Wodehouse (the Jeeves books, but he has a much bigger bibliography) are starting to become available online as they started publishing in the 1910s and 1920s (books up to 1922 are public domain in the U.S.).
I am starting to read some Dickens and liking it more than I had anticipated based on my high school experiences. Hard Times is pretty satirical and I was surprised how many of Dickens' criticisms of education and the economy are still relevant today. I just finished David Copperfield and was surprised how much I liked it. David Copperfield is most famous for the segment at the beginning describing David's awful, abusive childhood (his terrible boarding school, the factory where he is sent to work) but actually that is only 13 chapters out of 64 and most of the book is about other things. The characters are really vivid and there are a lot of strong female characters. There is also plenty of melodrama--this is Victorian literature, after all--and at one point Dickens is clearly running out of book and needs to wrap up a bunch of characters so he just loads them on a ship and sends it to Australia. But it has really stuck with me...
There are also some real stinkers out there...sometimes the prose is just too hard to read, and sometimes the attitudes about people of color etc are so out of date it really grates (there is more of that than I had remembered in the Sherlock Holmes stories for instance, and Walter Scott's attitude toward the Jewish characters in Ivanhoe was appalling). I also stay away from the public domain translations of non-English language books because the Victorian translators had a tendency to edit out "ungenteel" material. There's still a ton of great stuff out there, though!