I find that Google Drive is my friend. It's easy to set up folders for each project, and then share specific files and/or whole folders with individuals using only their email address.
Drive also offers a lightweight app to integrate with your OS, much like Dropbox. The advantage that Drive affords users over Dropbox is that Google Docs integrates so seamlessly, so sharing body copy, imagery and designs with colleagues and clients alike is intuitive.
If the coder has access to Adobe CS software, then I will send through the native docs, otherwise JPEGs scaled to different sizes, typically annotated to highlight specific requirements.
For making changes to files, you really want to use some form of version control. The most popular is GitHub. I've only recently integrated this in to my own workflow, and it's one of the best things I've done! Again, this can be configured to share content with individuals and groups.
Granted, this isn't as accessible as something like Google Drive, but if you commit a few hours to getting up to speed, you'll wonder how you ever coped without it! I can't recommend 308tube's videos enough. Make notes whilst watching the first two videos and you'll be well on your way.
The best thing that I find with this workflow is that I can access all my work from any computer with an internet connection, it's all backed up on the cloud, and I can easily share content with whoever needs to evaluate or contribute to the workload.