Many people use Twitter as their primary online identity. For various discussion platforms, commenting systems, websites and services they have opted to "Sign in with Twitter" rather than create a platform-specific profile. As a result, when Twitter goes down, they are without an identity to access all of these sites.
Of course, when Twitter goes down "influence metrics" services like Klout, Kred, or PeerIndex go down as well. Academic research relying on pulling real-time data from Twitter is interrupted as are platforms aimed at providing data to researchers, like 140Kit. Social analytics firms that provide data to corporate clients, like SocialFlow, Gnip, and 140Proof, crash as well. When you are worried about the validity of your data, an interruption of this kind can force you to re-start from square one.
As these first-order systems that rely directly on Twitter data streams go down, a range of second-order systems that rely on those APIs cease to function as well. The increasing interdependence of the social web, virtually assures that when a service as central as Twitter goes down, ripple effects widespread. I can't tell you the amount, but I guarantee this translates into lost revenue, data, and man-hours for a lot of people.
Thankfully, the world can survive for a few hours without data for targeting ads. Twitter is not so deeply imbedded in the infrastructure of our lives so as to make this a catastrophic event. But what if it were? For example, Ushahidi, a real-time crisis-mapping platform has been successfully deployed to record violence in Kenya and the Congo, and to help target aid resources during the 2010 Haitian and Chilean Earthquakes. Ushahidi allows people to report on the ground conditions by collaboratively updating a map by posting from Twitter, among other platforms. Had Twitter gone done during a crisis of this type, it may have meant far more than lost ad revenue or me having that anomic feeling of being unable to share my every thought.
Additionally, several start-ups like TwitPay and Chirpify are working to leverage Twitter as a platform for commerce, by allowing customers and business to transact via tweet. While these types of "more serious" Twitter uses remain relatively rare, it is a very real and growing segment. As we move towards a future increasingly facilitated by services like Twitter, we should keep completing the phrase in our minds "When Twitter goes down..."
High degrees of interconnectivity create the possibility for systemic risk. As we can see in the (luckily) fairly trivial case of todays twitter crash induced cascade, failure of an important node within this increasingly interconnected space leads to significant down-stream effects. If we continue down the path that Ushahidi and Chirpify suggest, in which Twitter is central to the functioning of high-impact, time-sensitive capabilities, systemic risk will become a serious concern. And it will require an attendant level of risk-management regulation and oversight. The question then becomes: At what point is a for profit-service so interconnected and critical that it should be thought of as something more akin to a public utility?