iOS 4.3 already supports this but only with songs, music videos, apps, and books purchased through the iTunes Store. According to Dropbox's support site, this
is how you "sync" content loaded on your Dropbox account without needing a PC. Whether or not this actually syncs the content so it can be accessed outside of the Dropbox app is another story.
64GB iPhone 5 | 64GB iPad mini | AppleTV 2 (2012) | AppleTV 2 (2010) | 2012 15" MacBook Pro, 1TB SSHD, 16GB DDR3 1600 MHz, OS X 10.8.3 Mountain Lion | Apple Lossless | iTunes AAC 192kbps VBR | iTunes 11.0.2| Library size = 1.04TB | Legacy iPods: 3G 40GB, 4G 40GB, 5G 60GB, 160GB iPod classic (2009)