Search-Engine-Synergy Virality (or Pseudo Virality depending on your definition)
If you broadened the definition of virality to include growth of new users through the actions of existing users, another form of virality would be what I might call search-engine-synergy virality.
In this model, users create content that gets indexed by search engines. Then, the site converts enough new search visitors to become content contributors, thus increasing the rate of highly indexed content, thus further increasing the number of search visitors as the rate of user conversion holds (or ideally improves).
By managing attrition to include both a) users who continue to actively post quality content and b) how long content items remain highly ranked, you can end up with an impressive growth curve driven by users rather than marketing budget.
This model is well suited to Q&A sites, blogging networks, and wikis with examples including Wikipedia, Quora, and StackOverflow.
The biggest difference with this pseudo virality is rather than users knowingly passing on the service through word of mouth or invites, they’re passing it on unknowingly as a byproduct of content exchange. But the similar fact remains in both models that the service grows rapidly through action of its users seeking value, rather than through traditional marketing and sales channels.
Another big difference is this type of virality relies on an intermediary, search engines. This introduces dependency risks that if not managed (e.g. by eventually getting users to access your site directly through an app rather than a search engine), can result in major loss of business with a search algorithm change.
Your position is improved if you can reach enough scale that search engines rely on you, too, since their users will receive value through their ability to access your content. But the balance of dependency is still far from center.