Dropbox is among the few major services which don’t have an official Windows Phone app yet. Worry not, the ever-growing community of Windows Phone devs has come to the rescue. Prashant Cholachagudda
has released CloudyBox, a dropbox client for your Windows Phones. You can upload, delete, share and download files. You can also view your dropbox usage and send referral links. Until Dropbox releases an official app, this seems like a great replacement.
You can get it at the marketplace link.
(beta marketplace. See comments for more details. Sorry for the confusion!)