Basic Authentication is considered a bit of an anti-pattern these days, but it can still be useful in a pinch when you have limited options for integrating with APIs, third party applications or the dreaded legacy applications.
Basic Authentication should never be a recommended solution, however I have met many clients who are still running services that use it and third party applications who only support basic authentication. Some security is better than none, right? I guess that's debatable.
If you want a modern identity solution, check out Identity Server. Identity Server is a one time configuration that will allow you to create your own OAuth, OpenID Connect or WS-Federation Authentication Server (aka Identity Provider, Security Token Service, etc), that can reliably service all of your applications.
This article will cover the theory behind basic authentication, including why we shouldn't really be using it, and then look at how we can integrate it into our OWIN pipeline.