Note: It seems like Dropbox has removed this feature in favour of the black icon. Dropbox has responded to my request with the following information:

If you like your desktop to look clean and slick you’ll probably get a little annoyed at the bright coloured logos in your menu bar! The Dropbox one is rather annoying compared to all the other nice flat, black and grey icons.
Screen Shot 2014-03-18 at 11.21.41

So how do you achieve this? It’s actually ridiculously simple!

Navigate into the Dropbox preferences and simply select the “Use black and white menu bar icons”
Screen Shot 2014-03-18 at 11.19.00

Now I am back at peace with my menu bar.
Screen Shot 2014-03-18 at 11.21.31

Dave Macaulay
Dave Macaulay
I'm an enthusiastic, slightly eccentric Magento developer who bores with the idea of another basic brief.