I would save it on your hard drive, email a copy to yourself, rip a copy to CD/DVD and give it to a friend, use a thumb drive, and basically make as many copies as you can in different places. I was a bit…paranoid…when working on my own dissertation.
In addition, I would compile (ctrl-E) everything and back that up at the end of every work session.
Edit: you will definitely want to read the stickied post about using Scrivener with dropbox. Personally, I’d use it as a backup, but I don’t think I would actually edit my file while stored on any cloud service. Or, rather, make sure you’ve got a backup somewhere first.
The more copies you keep updated and backed up, the better.