GitHub has been offering an official GitHub app for Mac OSX from quite a while now, and now they have launched one for Windows as well. Git on Windows has never been as well supported as it has been on Linux, however now with an official client for Windows there is a good set of tools including a GUI for Windows as well.
The new GitHub app features all the Git command line tools, and even comes with support for PowerShell — which is Microsoft’s answer to Linux’s much better command line shell. With its integration with PowerShell it can offer auto-completions for Git commands, making it much simpler to use via the command line. While it does offer integration with PowerShell, one can also optionally use the standard command line, Git Bash, or even a custom command line tool such Console2, PowerCmd etc. While it provides these convenient wrappers, it uses the standard msysGit version of Git tools.
The GUI offered by GitHub features a Metro-inspired interface. It is closely integrated with GitHub. You can log into GitHub with the client, and with one click clone any GitHub repository into a predefined directory using the GitHub GUI client. Updating — or Syncing — repositories, creating and browsing branches, browsing history, committing changes etc. all can be done using the GUI.
While support for GitHub is integrated, it does fully support non-GitHub repositories as well. It can easily be used with other providers, but without the same level of integration.
For those looking for a Git GUI for Windows, another good software package is TortoiseGit which offers integration with Windows Explorer.
You can find out more about GitHub for Windows, and download it, from the GitHub Windows page.