GitHub: 'No supported authentication methods'

After jumping aboard the Git(Hub) bandwagon yesterday, I downloaded TortoiseGit (and msysGit) for Windows to serve as my Git client. When trying to push to GitHub, I was was confronted with:

No supported authentication methods available (server sent: publickey)

I spent an hour scouring Google and troubleshooting to no avail. Thankfully, I somehow managed to discover that problem was not in msysGit or TortoiseGit, bur rather in my PuTTY configuration. After resetting PuTTY's default settings by removing the HKEY_CURRENT_USER\Software\SimonTatham\PuTTY\Sessions\Default%20Settings key with regedit, pushing through TortoiseGit worked like a charm.