About a year ago I went on a systematic search for the best online file storage services. I tried all the most recommended ones and Dropbox came up head and shoulders above the rest, for the following reasons:
1. It's free account is extremely generous – 2GB and no individual file size cap.
2. The automatic-syncing with folders on my computer makes sharing and backing-up extremely convenient.

So from my perspective Dropbox has grown so much because it offers a much better service than its competitors.

Interesting to hear about the 'secret sauce'; I didn't know that.