I might be wrong about this, but isn't it only considered a monopoly if the aforementioned company is using its massive usershare to shut down competitors unfairly? Facebook is a free service, so it's not undercutting other sites. They're all allowed to get themselves lots of users too, if they can figure out how.
The fact that social networks gain value with users means the solution isn't to "break up" a site like Facebook. That only worsens everything for users.
Technically, it might still be considered a monopoly, but having a monopoly is not against the law. It is illegal to "abuse" a monopoly position in one market to gain advantage in another one, or to "unfairly" shut out competitors, as you describe. What got Microsoft into trouble was attempts to use their monopoly to threaten PC makers who wanted to install Netscape, for example.
("abuse" and "unfairly" in quotes because there is a lot of complex legal code defining these things, but I think this is the general idea.)
I don't really know if it massively happening, but less and less people use photo-sharing sites. It's not the quality of photos that count or the availability of Flickr plugins etc, it's
1) the fact that you can do it in Facebook now, so it's easier
2) you can tag your friends (and there's now way to do it for external data, or to put this info out of facebook through APIs)
It's hard to make that case, because ownership of data is ambiguous. For instance, if I have my phone# on my profile, and you sync it with your mobile device, fine. If you take my contact details and add them to your address book on another site, well that's not so fine. But is my phone number my data or yours in this scenario? Looking at my photos on FB is fine. Posting one of my photos on your wall or making it your profile pic is fine. Uploading it to another site in your own gallery... But didn't I put that photo on the Internet for all to see? Well, perhaps not, if I set it "friends only" on FB then there was probably a reason for that. A chain is only as strong as its weakest link.
Facebook's technology and the terms of use of its API attempt to strike a balance for issues like this. Interoperability is fine on paper, but FB isn't just a website; it's a part of the plumbing of people's real lives.
The fact that social networks gain value with users means the solution isn't to "break up" a site like Facebook. That only worsens everything for users.