Software systems of today are frequently composed from prefabricated, heterogeneous components that provide complex functionality and engage in complex interactions. Existing research on component-based development has mostly focused on component structure, interfaces, and functionality. Recently, software architecture has emerged as an area that also places significant importance on component interactions, embodied in the notion of software connectors. However, the current level of understanding and support for connectors has been insufficient. This has resulted in their inconsistent treatment and a notable lack of understanding of what the fundamental building blocks of software interaction are and how they can be composed into more complex interactions. This paper attempts to address this problem. It presents a comprehensive classification framework and taxonomy of software connectors. The taxonomy is obtained through an extensive analysis of existing component interactions. The taxonomy is used both to understand existing software connectors and to suggest new, unprecedented connectors. We demonstrate the use of the taxonomy on the architecture of a large, existing system.