Motivation: There is a growing need in bioinformatics for easy-to-use software implementations of algorithms that are usable across platforms. At the same time, reproducibility of computational results is critical and often a challenge due to source code changes over time and dependencies. Results: The approach introduced in this paper addresses both of these needs with AlgoRun, a dedicated packaging system for implemented algorithms, using Docker technology. Implemented algorithms, packaged with AlgoRun, can be executed through a user-friendly interface directly from a web browser or via a standardized RESTful web API to allow easy integration into more complex workflows. The packaged algorithm includes the entire software execution environment, thereby eliminating the common problem of software dependencies and the irreproducibility of computations over time. AlgoRun-packaged algorithms can be published on http://algorun.org, a centralized searchable directory to find existing AlgoRun-packaged algorithms.