Global outages or reductions in service quality are very rare these days. Regional outages happen from time to time but are not very common. Local outages are frequent, but irrelevant -- the Internet is meant to be resilient to local outages, which presupposes that local outages are a common concern. Obviously if you shrink your scope enough you will be able to say problems happen regularly -- considering only the connectivity in my home there are many incidents each year.

The most significant incident in recent memory involved a severed fiber optic line in New York City earlier this year, which affected the US Northeast in various ways. The impact was relatively short-lived, and despite living and working in NYC I was not personally affected at all -- even though I use Verizon FIOS and the line in question was operated by Verizon (a testament to how resilient Verizon's own network is). That is the mark of an extremely robust system -- a major, overly-centralized component (one cable carrying many supposedly redundant links) is destroyed and the effects remain highly localized and the impact is not universal even within the local area.