In bioinformatics, as well as other computationally intensive research fields, there is a need for workflows that can reliably produce consistent output, from known sources, independent of the software environment or configuration settings of the machine on which they are executed. Indeed, this is essential for controlled comparison between different observations and for the wider dissemination of workflows. However, providing this type of reproducibility and traceability is often complicated by the need to accommodate the myriad dependencies included in a larger body of software, each of which generally comes in various versions. Moreover, in many fields (bioinformatics being a prime example), these versions are subject to continual change due to rapidly evolving technologies, further complicating problems related to reproducibility. Here, we propose a principled approach for building analysis pipelines and managing their dependencies with GNU Guix. As a case study to demonstrate the utility of our approach, we present a set of highly reproducible pipelines called PiGx for the analysis of RNA sequencing, chromatin immunoprecipitation sequencing, bisulfite-treated DNA sequencing, and single-cell resolution RNA sequencing. All pipelines process raw experimental data and generate reports containing publication-ready plots and figures, with interactive report elements and standard observables. Users may install these highly reproducible packages and apply them to their own datasets without any special computational expertise beyond the use of the command line. We hope such a toolkit will provide immediate benefit to laboratory workers wishing to process their own datasets or bioinformaticians seeking to automate all, or parts of, their analyses. In the long term, we hope our approach to reproducibility will serve as a blueprint for reproducible workflows in other areas. Our pipelines, along with their corresponding documentation and sample reports, are available at http://bioinformatics.mdc-berlin.de/pigx.