By Steven R Brandt.
There is a new trend toward making papers executable; that is including (some fraction) of the code needed to produce the results within the text itself. This makes it easier to understand, verify, and build on previous work. In addition to making code more reproducible, these novel forms of publishing will encourage scientists to follow better coding practices, and to make it clearer which software packages support a given work (so that they can get appropriate credit).
The executable paper concept was recently given a boost in the Elsevier challenge of 2011. As yet, followup by the publishing industry has been limited.
The following is a list of journals that are moving this direction and are making some experiments with new forms of publishing scientific content. Publications qualifying for this list should have some form of review, and should make verifiable code part of the publication. This list of journals is not exhaustive - if you know of others, please let us know.
ACM Transactions on Mathematical Software (TOMS) has a replicated computational results initiative (RCR), which offers a special designation to those papers which complete the process.
The Mathematica Journal, which publishes Mathematica Notebooks.
In addition to these existing publishers, there are a few who have promised to move more toward executable papers in the near future.
O'Reilly has promised to embrace Jupyter notebooks.
Nature also appears to be considering it, and has been experimenting with interactive content through PDF.
Sometimes supplementary electronic content, such as an IPython or Jupyter notebook, is made available alongside the paper. Frequently, the content is stored externally on sites such as nbviewer.ipython.org or github.org.
Thanks to participants at the WSSSPE3 workshop for brainstorming the question originally.