Funding and users are flowing to services that claim to put members in charge of their personal data.
The rivals range from start-ups to more established firms working on the specifications for an ecosystem of open social networks.
Experts say Facebook may have little to worry about, despite 11,000 people pledging to quit Facebook on 31 May.
"Nobody has reached anything like critical mass in the same social platform area," said Lee Bryant, from social technology consultancy Headshift.
"Facebook is like an entire web operating system," he said.
There are already many well-established alternatives to Facebook.
Fans of the microblogging service Twitter might argue that it is poised to steal the site's crown. It entered the world's top 100 websites only last year, and is now sitting around tenth position globally, according to Alexa, a web information company.
But Twitter is more a micro-blogging site than a social network, where friends follow each other's daily activities by default.
Alongside are a whole host of other early high profile innovators in social networking.
But many, including Bebo, Friendster and Myspace have seen their popularity decline in the last 24 months. None of these are still in Alexa's global top 20.
The latest round of privacy issues with Facebook has provoked considerable interest in some more embryonic social network projects.
Mr Bryant said: "Many people are looking to Diaspora as a new model - something which is standards-based, open-source and distributed."
Diaspora was founded in early May year by four New York University students who aim to create "the privacy aware, personally controlled, do-it-all distributed open-source social network".
It also caught the eye of investors on the Kickstarter website, which aims to find funding for creative projects. In just a few weeks, the Diaspora team has received pledges of $175,000 (£122,000). They started out asking for just $10,000.
Max Salzberg, one of the founders, told BBC News: "Facebook is not what we are going after.
"We are going after the idea there are all these centralised services where people are giving up their personal information. We want to put users back in control of what they share."
But Diaspora's software is still in the early stages of development, and it's not yet clear exactly where the project might go.
Another fledgling social network is OneSocialWeb that has the backing of mobile giant Vodafone.
Its designer, Alard Weisscher, told BBC News "We believe social networking is becoming so important ... that users should have the right to choose their provider, be able to switch between providers ... whilst owning and being in full control of their data."
Mr Weisscher said that rather than try to create a new social network, the OneSocialWeb team is trying to define a common language, called protocols, for communication between social networks.
This is an idea common to many such projects.
Michael Chisari founded Appleseed in 2004, to try and build a simple social network. The question he pondered at the time was "If two sites were running my software, why couldn't they interact?"
Like Diaspora, Appleseed's approach is one of a growing band of "distributed social networking" projects, where anybody can set up a social network, and the different systems should be able to interact with each other.
Mr Chisari said: "I compare it to the 1990's, when AOL and CompuServe (early Internet Service Providers) were both very popular, but were 'walled gardens'".
"Users on AOL could only e-mail other AOL users, same with CompuServe. Then, e-mail started getting popular and some people switched, but it forced people to ask why they were being walled off," he said.
Mr Chisari pointed out that both AOL and Compuserve "were forced to open up ... so that their users could participate with the rest of the world."
Both companies have since faded considerably, and Mr Bryant at Headshift thinks something similar might happen at Facebook: "It's a real and present danger. What people are looking for as a sign of that is a flocking behaviour.
"It was a flocking behaviour that built Facebook, and it's a flock of people saying they're going to a different social network that could lead to its decline."
So can the new social networks establish a set of standards that they all stick to?
Mr Bryant said it is a sensible goal in the long term. "But over the short term, it will be a real battle."
The founder of Appleseed has discussed universal standards with OneSocialWeb, because the software he developed has some similarities to their social networking language.
But well-funded Diaspora has indicated that it might use its cash pile to implement a different set of open standards called OStatus.
Those are being developed in part by yet another potential rival to Facebook.
That company is called StatusNet, which itself has created social networking software in use by 25,000 sites, with more than 1.5 million user accounts, according to Evan Prodromou, the company's head.
"Any StatusNet site lets people from other (OStatus standards-compliant) sites follow the users there", he said.
"The open protocols that we use mean our software works with much higher-profile services, like Google Buzz, Posterous, LiveJournal, WordPress, and Tumblr."
Is there any chance that Facebook might sign up to such an open model as well, just as AOL and Compuserve did with E-mail?
Mr Bryant from Headshift thinks not: "The valuations we've seen for rounds of investment in Facebook mean they have to focus on making money soon.
"If they go down the open standards route, they would lose much of the lock-in that gives them value," he said.
And any such move would also assume that a common, open language can be established in the first place.
According to Mr Prodromou from StatusNet, a "federated social web summit" is planned in July to try and build momentum for one around OStatus standards.
However, he said, it would be "invite-only".
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