Is it possible to run games over remote desktop?

Technically OnLive does this, but they have custom silicon in ridiculous data centers that can encode HD video with 1ms latency. Any traditional VNC is going to incur enough latency in compression and transfer to make any real-time game unplayable. Solitaire will still work fine.

Some VNC clients for Windows are RealVNC, TightVNC, and TeamViewer.

It shouldn't matter all of the rendering will be done on the remote machine, it will just bring the output to your monitor. You should be fine playing any game the remote computer can handle. I play Civ 4/5 over team viewer all the time. Your only problem will be if you are accessing this PC over a WAN, you may get choppiness due to network latency.

For the more tech savvy installing a "Gaming Anywhere" server and client may be useful: http://www.gaminganywhere.org/index.html

I¡d suggest to take a look at the performance experiment they did; the figures are quite impressive except for network load that is sometimes very slightly over the already deceased OnLive or StreamMyGame. http://www.gaminganywhere.org/perf.html

They offer pre-compiled binaries for win 32 bits and linux 32 bits, and an alpha for Android.

It's open source and free.