FWIW, Dropbox actually DID replace my USB drive (99% of the times at least).
What Dropbox replaced for me is the 'My Documents' folder. It allows me to access my files on my work PC, my laptop, my iPad, my iPhone, or anyone else's computer that has an internet connection.
At one point during the setup of my new gaming PC, I somehow hosed things to the point where I couldn't install Windows (motherboard BIOS update, maybe?). I was getting driver detection failures during the install process, my peripherals (keyboard + mouse) wouldn't work, no NIC functionality, my CD drive was unusable. I ran out to Walmart at 1AM to buy a 16GB USB drive/16GB SD card, tethered my phone (my only functional computer at the time) to my PC, downloaded the required ISO to my phone's new SD card, moved the ISO to a USB via a live instance of Ubuntu running off of another USB, and installed Windows via USB (and things magically worked from there).
Dropbox is fantastic, but USBs aren't dead.
What I use dropbox for: Lazy backup system (all my important code is symlinked there, sharing small files (<20mb) over the net
What I use USB drives for: Sharing large files (>100mb) between local computers, liveUSBs