I just started to work on Git. I use windows 7 and has installed msysgit(1.7.8) and Tortoisegit(1.7.6). The repository is created on Linux server which is accessible thru LA
Please not the URL of the repo remote origin can cause this problem. I had an old repo that worked perfectly and a new one I just cloned that was asking me for password.
Upon comparing the information in Settings > Git > Remote > Url I saw that the one which worked had:
git@github.com:githubAccount/repoName.git
The new one that did not work had an https address.
Please see screenshot below as well.