Different programming paradigms, such as object-oriented, functional, and procedural programming, influence software development by shaping how developers approach problem-solving and code organization. Each paradigm offers unique methodologies and best practices, impacting how software is structured, maintained, and extended. For example, object-oriented programming promotes code reusability and encapsulation, while functional programming emphasizes immutability and higher-order functions, allowing developers to choose the paradigm that best suits their project needs.