Instead of hosting my company's source code on Github, I would like to host it on our intranet under our control.
What software could I use to simulate the same kinds of Git-based source-control features that are offered by sites like Github?
Ideally this solution would be associated with a Ruby-based web application.
Depending on whether you want a feature-for-feature clone of GitHub, or just somewhere to view Git repositories alongside an issue tracker, wiki, etc., I'd recommend either using Gitorious (the GitHub clone) or Redmine.
Many of the advantages of GitHub (easy forking, user follows, etc.) aren't usually very applicable inside a corporate firewall, so you may find a more traditional software workflow tool like Redmine as or more useful for plain source code management, while offering better functionality for project wikis, issue tracking, and access control.
Also, if you really want the GitHub feature set, why not simply pay them for either hosted private repositories, or go all the way and license GitHub Firewall Install? The up-front cost may seem a lot higher than a DIY solution, but I can say from experience that setting up and administering any of the OSS solutions in this problem space can be a time-consuming distraction from your real work.
Among full fledged git hosting solutions beside mentioned Gitorious (in Ruby), there is also InDefero (in PHP), and repo.or.cz duct-tape called Girocco (Perl, mainly).
If you want just git web interface, there are many more: gitweb (Perl), cgit (C), git-php and ViewGit (PHP), Ginatra (Ruby, using Sinatra framework),...
It depends on what you mean by simulating Github's feature set. The design? The number of users?
I'd rather have a look at the alternatives and what kind of features they have, maybe even try them out for a while. On the other hand: if what you want is Github, you should get Github.
Disclaimer: I contribute to Gitorious.