Common programming paradigms used in software development include procedural programming, object-oriented programming (OOP), and functional programming. Procedural programming focuses on sequences of steps to achieve a task, while OOP organizes code around objects and their interactions, promoting reusability. Functional programming, on the other hand, treats computation as mathematical functions, emphasizing immutability and pure functions. Understanding these paradigms helps developers choose the most suitable approach for specific projects, influencing code structure, maintainability, and collaboration among team members.