I am new to Dropbox, and I'd like to know if there is an easy way to access Dropbox content from SharePoint 2010 / Office 365.
For example, should I consider BCS? Or is there a way to work with the Dropbox API?
DropBox does have an API with a REST interface - described here. I think REST may be the way to go compared to BCS.
There's an article showing how it is used (via .NET) - Create, delete and move folders with the Dropbox REST API.