I have used RealVNC viewer. It's free and they are updating it relatively often - not that I have encountered too many bugs with it. In case of some connection hickups, it'll mess up the the graphics for some time, but any activity - moving window, for example - fixes that, so it's only a very minor annoyance. Your requirements:
- Support touch, of course. Yes.
- Be relatively fast to use Yes. This is obviously a bit ambiguous. Using remote GUI over a very slow connection - say GPRS - is not too good, but it still works.
- Work with computers running Server 2012: yes.
- Support multi-finger gestures: yes, at least zooming and scrolling. See help page.
- Free is always nice: yes, it's free.
I have nothing more to say about it - it works fine - so there's feature list from iTunes:
- Interact with your computer as though sitting in front of it.
- Support for Bonjour, making it simple to locate and connect to compatible computers.
- Give connections user-friendly names, and see desktop previews.
- Pinch to zoom in to a specific area, or out to see the whole picture.
- Easy navigation, scrolling, dragging, and selection using standard touch, tap, and drag gestures.
- Mouse button mode for precise control over mouse button and scrolling operations.
- Easy text entry using on-screen keyboard with preview.
- Important non-character keyboard keys (function, modifier, and so on) available on a scrolling key bar.
- Automatic performance optimization.
- Support for screen resolutions up to 5120 by 2400 pixels (though the actual resolution is limited only by the memory of your device).
Of course, it is not RDP client, so you need to install VNC server to your Windows machine. Doesn't have to be RealVNC.