What is the simplest (to install and use) git client for Windows nowadays?
Apart from others have already said, there is also SmartGit.
msysgit is, like everyone else said, wonderful.
You should also look into Git Extensions for visual studio integration, which I find I can't live without.
msysgit and TortoiseGit / GitCheetah
I just use the one in Cygwin, although many people are looking forward to msysgit once its out of the preview stage. If they make it a no-brainer to install (like in Cygwin), it would be nice.
I had serious issues with negotiating SSL connections with msygit+putty. It's so much easier on cygwin. I even wrote up a guide on it. See Windows Git Tutorial: Cygwin, SSH and Projectlocker.