I don't see it growing as big as Google or Facebook either, not because the product sucks (when I used it last, it worked well), but simply because I don't think many people have a real need for it.
My parents use Google, they reluctantly signed up for Facebook (and got bored and stopped using it), but they'll never have a need for Dropbox. Nor will any of their friends, or most of my friends.
With the trend towards appliance computers and walled gardens, users interact with their file systems less than ever. Their tagline is "Never email yourself a file again!" I can't remember the last time I emailed myself a file. It might as well be "Never transfer a file between computers using a floppy disk again!"
When I was a student, and I had a desktop, a laptop, and lab computer, Dropbox came in handy on occasion. Now, I have a laptop and tablet. What would I sync between my them? Photos? Music? Notes? Cloud sharing is built in, and it's less of a hassle than going through Dropbox.
I'm sure there are people for whom it is essential. But those people are probably in the minority, and their numbers are likely to dwindle.