Dreamwidth is an LJ fork in that it's based on the LJ code, but it has a lot of improvements (http://wiki.dwscoalition.org/wiki/index.php?title=Dreamwidth_changes_from_LJ), like separating the friends list into access list (people you want to read your locked posts) and subscription list (people whose posts you want to read). Plus it is ad-free. It's run by two ex-LJ employees, so they know the code well and know what they want to change. Its mission statement is much more user-friendly than LJ's, in that they say they will treat users as people and not as a commodity.

The website is http://dreamwidth.org/ and a number of people have written journal entries explaining why they're moving to Dreamwidth (http://wiki.dwscoalition.org/notes/Why_Dreamwidth).