I suppose I should answer that question myself, if I'm asking others, so...
I just installed the latest snapshot for use at my workplace. I know a lot of people want an easy way to keep a journal, worklog, set of scribbled notes, etc -- that alone would merit a tool like this - but the ease of tracking other people's journals makes it a killer groupware app in addition to a personal productivity tool.
One of the biggest problems we have, like a lot of tech companies, is knowledge transfer. People are too busy doing stuff to share what they know, and there's always too much to know. Thus anything that encourages people to publish more information, in ways easily accessible to others, is a good thing. Email is often used for this, but it's often the wrong medium; you don't want to choose who to push the information to (and invariably get the wrong set), you want to publish it and let people search it or browse it or subscribe to it as they choose. Kinda like LiveJournal.
Also, it's just useful to know what your coworkers are up to on a day-to-day basis (or hour-to-hour) if you choose. (Actually, that'll especially appeal to managers...)
My initial plan was to set up the server, get a half-dozen or so people hooked on it, and let it spread virally from there. I introduced Jabber (an open instant messaging system) that way, and now we have a couple hundred users. But when I showed LJ to my manager, he immediately thought of a couple uses for it, so it might become an actual Project that I can spend time on without coming in on weekends. :-)
I also have a personal agenda in introducing LJ, but the rambling speculations on how groups are influenced by their communication media and why LJ may be good in that regard ought to wait for another time.