UPDATE | 3:30 PM: After service was restored, Cloudflare issued the following statement (via TechCrunch):
Cloudflare CEO Matthew Prince also offered a biting take of his own on Twitter:Earlier today, a widespread BGP routing leak affected a number of Internet services and a portion of traffic to Cloudflare. All of Cloudflare's systems continued to run normally, but traffic wasn't getting to us for a portion of our domains. At this point, the network outage has been fixed and traffic levels are returning to normal.
BGP acts as the backbone of the Internet, routing traffic through Internet transit providers and then to services like Cloudflare. There are more than 700k routes across the Internet. By nature, route leaks are localized and can be caused by error or through malicious intent. We've written extensively about BGP and how we've adopted RPKI to help further secure it.