I have successfully cloned Git repository in Jenkins over Git/SSH on Windows 2008 32-bit. When I tried to do the same on Windows 2008 64-bit, Console Output page ge
Since my Windows Jenkins was a slave, I needed to configure that node to find the git in cmd instead of bin as described by inger. To do this, go to Manage Jenkins, Manage Nodes, click on the appropriate node, click on Configure and then go to the Tool Locations. Find git in the drop-down and then specify the path to git.exe (including git.exe), like C:\Program Files\Git\cmd\git.exe.
I confirmed that the cmd/git.exe worked differently than the bin/git.exe from both command-line and with a temporary jenkins job using the git command (instead of an scm repo).
If your account is attached to domain. Then you need to make sure user for which the Jenkins Slave is ran. For the purpose open Settings->Properties of "Jenkins Slave"->Log On. and choose necessary user from domain for correct execution.