The most common types of software testing include functional testing, which focuses on user experience and ensures the application works as expected, load testing, which determines how much volume a software can handle before breaking, security testing, which checks for internal and external threats and strong authorization processes, accessibility testing, which verifies an app's accessibility for differently-abled groups, exploratory testing, performed informally by teams to discover new bugs, and continuous testing, which involves testing throughout the pipeline. These types of testing are crucial for integrating quality into a software development pipeline.