Steam on Linux Beta on Ubuntu 12.10
I finally got around to installing Steam for Linux because Valve had open up the Steam On Linux Beta to everyone - yah! I'm happy to report the Steam Client starts up fine on my Ubuntu 12.10 Linux x64 system. I applied one workaround for getting videos to play (Adobe flash workaround for x64 bit systems).
For a few years I've been using the Open Source Linux drivers, because the AMD Catalyst Drivers would cause black screen lock ups. I decided to be brave and install the latest AMD Catalyst Drivers even though they've been classed as Legacy on Ubuntu 12.10, I found some instructions here which worked for me.
I've yet to try an installed game. I can't install Team Fortress 2 as that requires 10GBytes of space which I don't have available on my Linux partition.
But I've managed to use the Steam Linux client quite easily looking around the Greenlight area. I tried the Big Screen mode and tried to drive with an Xbox 360 wireless controller to navigate. The Bigscreen mode worked to a point and then crashed, and the Xbox 360 controller didn't have correct keys mapped.
So after a few hours investigation I've been impressed. If Steam for Linux really takes off I'll be really pleased.