Now, I said "finally" because I've been able to pop open a console from my browser for my Linode instance for quite some time. I was actually surprised that Amazon didn't have a similar feature.
It's not particularly onerous having to SSH from a terminal to an EC2 instance if you're on Mac OS X or Linux, but Windows folks don't have a default terminal/SSH client. That's a pretty big segment of Amazon's business, and I suspect more than a few AWS customers have grumbled about having to download PuTTY to get into their systems.
It turns out, MindTerm is a pretty nice little terminal emulator. It takes a couple of steps to launch the first time, because you need to point it to your key to access the EC2 instance (if you have a key, which you should). After that, you can have it launched in a couple of clicks.
Actually, it's a little more full-featured than Amazon implied in their post. You don't just get shell access, you can launch multiple shells (without needing Screen or Tmux) and use it to SCP/SFTP files to your EC2 instance as well.
Just go to the Plugins menu of MindTerm and choose SFTP or SCP file transfer. Then you get a simple dialog to transfer files up to your EC2 instance, no typing required.
If you're running a job in the main terminal window and want a second shell to do something else, go to File -> Clone Terminal or New Terminal.
It looks like you can also use MindTerm to set up an SSH tunnel to your EC2 instance as well.
Overall, I've been pleasantly surprised by how snappy MindTerm is and how full-featured it is. If you're using AWS and need to SSH into your EC2 sessions, give it a try next time.