A good API should support broad use cases across different platforms such as mobile, embedded, and web applications. It should be easy to use with high-quality documentation and follow best practices for defining API paths and methods. An API should also be reliable, secure, and scalable to handle traffic spikes and increasing requests. Additionally, it's essential to have versioning support to cater to both legacy and current versions of an application. To demonstrate how to build and observe APIs, a pet store API was created using AWS Lambda functions that call the existing pet store API, followed by creating an API gateway to trigger these Lambda functions. Lumigo monitoring and observability were also set up to monitor the deployed pet store API.