A large percentage of real-world software configuration issues, such as misconfigurations, involve multiple interdependent configuration parameters. However, existing techniques and tools either do not consider dependencies among configuration parameters - termed configuration dependencies - or rely on one or two dependency types and code patterns as input. Without rigorous understanding of configuration dependencies, it is hard to deal with many resulting configuration issues. This paper presents our study of software configuration dependencies in 16 widely-used cloud and datacenter systems, including dependencies within and across software components. To understand types of configuration dependencies, we conduct an exhaustive search of descriptions in structured configuration metadata and unstructured user manuals. We find and manually analyze 521 configuration dependencies. We define five types of configuration dependencies and identify their common code patterns. We report on consequences of not satisfying these dependencies and current software engineering practices for handling the consequences. We mechanize the knowledge gained from our study in a tool, cDep, which detects configuration dependencies. cDep automatically discovers five types of configuration dependencies from bytecode using static program analysis. We apply cDep to the eight Java and Scala software systems in our study. cDep finds 87.9% (275/313) of the related subset of dependencies from our study. cDep also finds 448 previously undocumented dependencies, with a 6.0% average false positive rate. Overall, our results show that configuration dependencies are more prevalent and diverse than previously reported and should henceforth be considered a first-class issue in software configuration engineering.