Yes, this has been happening for several days. InsaneJournal, which uses LiveJournal's software but is independent, reports that it has received a "mass influx of users." I assume that the same is true at GreatJournal and JournalFen, where fans are also migrating. In addition, there are various attempts to start a new fan-run LJ-clone. Other fans, though, seem determined to stick it out LiveJournal, or are taking the cautious approach of mirroring their LJ journals at other blogging networks.
 

I'm keeping my LJ account there, only to read the communities and people who are staying but I'll posting once, perhaps twice more. After this ... I don't know. I think I'll move to Blogspot on a permenant basis.
 

I've begun mirroring my personal journal on GreatestJornal, my writing journal will probably stay on LJ because it's in no danger of being targeted by their deletions at this point. If that changes then I'll probably move it to GJ as well but for now only my personal journal is getting mirrored. I also have accounts (unused but mostly to reserve my username) at all the other major journaling sites, DeadJournal, Insanejournal, Journalfen etc. So we'll see how things go, I like GJ the best of the options, though.