I use aNobii.
It's a very good site with a crisp clean interface. The site produces recommendations based on what books you have on your shelf. When you add a book to your shelf, you can categorise it as finished, not started etc, including dates of when you got it, when you started it and when you finished it. You can also tag each book to help navigate your collection & find other books with the same tag. Other fuctions include the ability to comment on a book, make personal notes & join groups.
You can see aNobii 'in action' as it were by clicking the 'my online bookshelf' link in my signature.