Github is great, and I think they've done a lot--for the better--to change and shape the way that everyone uses and does really awesome things with git.
But I worry about lock-in, I worry about having a project that relies on some feature of github that can't be easily accomplished on another platform.
This post is an index of "git ecosystem" tools that let you get something that looks a bit like github on your own servers. Feel free to edit this page (it's a wiki!) if you have other tools you like or can recommend!
Wiki / Pages
Github has a wiki system that's open source. I've never played around with it, because there's ikiwiki which is better anyway.
Their page's functionally is also open source, it's Jekyll there's no particular shortage of programs that do this kind of thing, and most aren't that good but that's an orthogonal point.
There are about a million different repository viewers, but the magic of the github website is that there's a lot of other integrated functionality (bug tracking, merge request queues, automatic forking/branching/etc.
I've only recently found notify-webhook, but it basically implements something like github's service hooks, as a traditional git post-recieve hook.
There's no great stand alone merge (pull) request system. Other code review tools are uneven, but the truth is that pull requests are not a sufficiently advanced code review tool.
Patchwork might work, but its a bit rustic for contemporary workflows.
Integrated issue tracking, hell any kind of issue tracking, remains an unsolved problem, but I think github's approach is a good start, and that feature set isn't as easily available from other projects/products/tools.