Windows equivalent of SSH

PowerShell comes with Remoting capabilities in WinRM:

PS C:\> enter-pssession otherhost

In XP, you could use PSExec, but this is only recommended over secure LANs:

psexec \\otherhost cmd

PuTTY for shell access.

WinSCP (UI, no cmd) for file transfers.

In order to connect another Windows computer using SSH, an SSH server would have to be running on the that computer. SSH isn't part of Windows, so this would have to be installed and configured. Take a look at Cygwin if this is what you're interested in doing. (Cygwin will also provide you a more familiar feeling command-line SSH, as well as other familiar Unix tools.)

If you're looking for the "Windows way" of doing these things, have a look at Remote Desktop (although it is graphical, not command-line based).

You can enable Remote Access on the target machine which will allow you to connect to it with Remote Desktop. You can also transfer files back and forth by mapping a drive back to your own computer if you configure your connection to allow access to local resources.

I've always felt uncomfortable advising the use of Cygwin for one single function. There is an alternative, however: freeSSHd. The project, unfortunately, is quite inactive, but it should be a match to Cygwin, especially if you don't want to clutter your PATH and other variables.

When installed and configured, you can use PuTTY for ssh access.