In terms of versioning, there aren't great products out there for that. Adobe used to have a product (maybe still does) but nearly all code versioning systems can't deal with tracking changes in binary files. They're really designed for text based documents.
You could use a product such as SharePoint or the like, but even those aren't great given how large PSD files can get.
The best you might come up with is 'asset management software'.
As for sharing work in terms of open sourcing it or public domaining your work, I'm not aware of a central web site for that. It's a good idea, though. There are a variety of places you can use for different types of works.
flickr allows you to share photos under a creative commons license
other stock photo sites such as http://www.sxc.hu/ let you share photos for free/open source
I think that we can take inspiration from the coding world on how to manage projects and teams for graphic design: coding reviews, commits, branches.
The main differences between coding and graphing are: tools and outputs. Both have many languages and grammars.
Have you tried GitLab http://gitlab.org for tracking and collaborating on graphic projects? It's like github but downloadable and installable on your serrver. It's about coding but maybe there is some sort of plugin/extension to customize it to the graphic world.
Behance and DeviantArt don't do most of this? I believe Behance has versioning, and you can set things up so others can download the file.
Also there is versioning and file sharing available with Adobe Creative Cloud. The advantage in Adobe CC is that you can actually view the file before you download it, and you can see individual layers (at least I know you can do that with Illustrator files. I haven't looked at my PSDs there to know if layers are individually viewable)