You can't work with it, because of liability. If you bless Dropbox and champion it to the rest of management, it becomes your problem when the inevitable data breach happens.
But you don't want to stamp it out all at once, because: 1. CIOs know that cutting off things people want really badly just leads to better circumvention tech (more people running proxies or using 3G laptops, etc) and suddenly you can't even watch what they're doing, let alone stop it.
2. Those things are useful. Just because the Enterprise can't make peace with limitations or find a suitable analogue doesn't mean those tools don't legitimately make people more productive.
So these people are trying to get a job done despite their manager's actions. A manager's job is to remove roadblocks to getting things done. In this situation, the manager needs to self-remove.
CIO's are adopting cloud apps. The reality is that users will still inadvertently save files in the wrong place. I know I do all the time. If we can help get the files into the right place, even if the user saves them in the wrong place, then that is progress and lessens the negative impact of rogue clouds.
Make it easy for people to do the right thing and don't make them change the way they work.
If it's such a big deal that employees are using Dropbox in the office, employ some of those Orwellian tactics bigcorps are so good at: block them. Block them and their entire CDN. Shut off access to Facebook, Google Drive and Box while you're at it. Make them use only corporate e-mail. Is being denied access (at work) to a service they purchased not ramification enough?
Shall we draw and quarter them instead? You're not powerless, you're just myopic.
I'd wager that if a corporation has a problem with employees using Dropbox, they've got problems with a lot of other stuff - so why not stamp it all out at once? Or, work with it! Embrace the growing cloud culture. Buy Dropbox for Teams, or Github Enterprise, or what have you. Clearly, your employees want it.
Or, disband the thought and grow up.
EDIT: Comment below generated while the site was not responding to requests.
> 503 Service Unavailable
It appears the "Shadow IT" has won this round.