It's been made clear in several posts that Stack Overflow (and other Stack sites) are not social media sites. This fact, I agree with. I don't believe SO should ever change that. However, I believe we can supplement it more with current social media avenues.
For example, we already allow questions and answers to be shared on sites such as Facebook, Google+, and Twitter. Sharing on social media can be useful for content on the site to be found, shared, and collaborated on besides the usual methods of discovery.
I'd like to take that one step further and allow users to link to social media in their profiles easily, and optionally. Facebook, Twitter, Google+, GitHub, LinkedIn, Stack Careers, etc.
Personally, I would like to have a link back to my LinkedIn, Twitter, and GitHub pages to complete my professional profile here to make sure I'm discoverable outside of the site, if need be.
I do realize that the "About Me" section can be utilized for this function, but I believe it would be easier to use the simple iconic branding people are already familiar with instead of scouring the About Me section to determine if you shared any links to these sites.