For websites, there are a few that come to mind:

1. 5 second test (do users understand what your site is about?)
2. Navigation flow (is the process of completing an action intuitive enough to help users help themselves?)
3. Click test (Is the interface following best practices for position of text, buttons, and forms?)

You can see best practices for each of these types of usability tests here:
https://usabilityhub.com