@Brian I like your definition. But I’m not sure about the strong focus on conversation. The conversational dimension is very important, but social media also allows for new ways of managing social relationships, knowledge or personal identities. For me, Wikipedia is a very important part of social media. But conversation is just a subordinate element of the encyclopedia. I’d prefer a more encompassing concept of media that is not only about content and conversation.

Traditional media is broadcast–one way. Social media enables interactions.

What comes out of those interactions should be described by other terms–conversation, empowerment, marketing, therapy, etc.

After much analysis, hosted conversations, wrestling matches, and continued research, I proposed the following definitions, which has served effectively for many practitioners still today:

Short Version:
Any tool or service that uses the internet to facilitate conversations.

Longer Version:
Social Media is the democratization of information, transforming people from content readers into publishers. It is the shift from a broadcast mechanism to a many-to-many model, rooted in conversations between authors, people, and peers.