Joggerjayne is correct. The only exception is where the author has been dead for more than (I think) 75 years - this is if they haven't signed over publishing rights. For instance, J M Barrie bequeathed the copyright (and thus all royalties) of 'Peter Pan' to Great Ormond Street Hospital.
But even given the 75 year rule, you still cannot reproduce later editions. For example, 'Pride and Prejudice' is long out of copyright and you could set up as a publisher and publish your own edition of it for sale or FOC. What you wouldn't be allowed to do is to scan, say, a twenty-year-old Penguin edition and distribute that.
The only sites I know of where current authors allow their books to be read FOC are the various writing websites and blogs. Authonomy is one such. You won't find any established authors on there but you may just come across the next bestseller. The site is owned by a large publishing house and they occasionally pick up new authors from there. It's like an online slush pile.
As JJ also says, if you find unauthorised texts uploaded, nobody can stop you downloading and reading them (actually, downloading may be illegal - not sure). But authors get precious little back on the cover price of a book in any case - often less than 10%, and that's if they're lucky. They make much of their money from workshops and personal appearances. And for every Dan Brown and James Patterson out there, there are probably a hundred more who are lucky to make a few thousand quid a year out of what they do.
As a wannabe bestselling author myself, I just think it's unfair. It's the literary equivalent of handling stolen goods. I mean, if you invented something and patented it, then someone pinched your stock and began to give it away, you'd rightly feel a bit miffed.
Libraries are mostly free, and many are now moving into the area of ebook downloads, so it's worth seeing what yours can offer.