I usually don't write tests for frameworks, databases, web-servers, or other third-party software that is supposed to work. I mock these things out, and test my code, not theirs.
If your software has a dependency on a third party component, then you should include that component in your tests. It's not about testing the component, it's about testing your integration with that component. For example, if you upgrade that component, and the API changes in a way that breaks your integration, you want your test suite to break as well.
Sometimes if a component is too slow or requires network access, you have to mock it out. But as a general rule, it's best to leave your dependencies in place.