Why? (Other than "all the cool kids are doing it", of course.)
Because there are all sorts of marvelous features. My favorites are detailed here.
Because, in addition to all its other increasing and well-documented issues, LiveJournal these days accepts crazy homophobic advertisers.
Because interrelation is easy. With the push of a button you can import your whole LJ, including comments, rather than having to start from scratch. LJ users can comment with OpenID on DW entries, and vice versa. You can have DW automatically crosspost to accounts on LJ and any of its various clones - and, if you go back and edit the DW post, it'll edit the others as well.
Because I've been waiting for a service like this one to come along for years.
In 2004, long before the cool kids were talking about leaving LJ, I went looking for an alternative. The one I found was GreatestJournal. In 2007, a traffic influx (thanks to Strikethrough '07) fried GreatestJournal's servers, and some time recently the site disappeared altogether. I didn't get backups.
I have a WordPress blog, but it isn't the same. From communities to flists to comment threads, LJ and its clones are just better at fostering interaction. So I've been watching every alternative (JournalFen, InsaneJournal, DeadJournal, Scriblit, and on and on...), looking for something that has that kind of organization, but with involved founders. Something with a reason for existence beyond "making money" or "not being LJ". Something, in other words, that I trust not to go the way of GJ.
And you know what? I trust Dreamwidth.
All of which is a lead-up to: I have invite codes to hand out! Comment if you want one, and I'll send a PM your way.
(You need a code to get an account. They're doing this to manage their growth, keeping traffic at a level that won't, uh, fry their servers. You see why I like these people?)