I think code examples are something that are best included in the "getting started" section of documentation. It gives the user a quick, usable, concise illustration of how to perform the most basic tasks. Sometimes that's all you need and this is frequently omitted by some software documentation.

Test cases are certainly useful if you need to dive into comprehensive/advanced usage of the API. But if you just want to "get started", a huge vat of unit tests can be daunting.