An updated Steam for Linux Client has been released by Valve. The client is stable, fixes a lot of bugs and improves the P2P networking.
A full list of improvements can be found here.
To install the latest Steam Client on Ubuntu 13.10 Saucy Salamander, Ubuntu 13.04 Raring Ringtail, Ubuntu 12.10 Quantal Quetzal, Ubuntu 12.04 Precise Pangolin, Linux Mint 15 Olivia, Linux Mint 14 Nadia, Linux Mint 13 Maya, Debian Sid, Debian Wheezy and Debian Squeeze, do this:
$ wget -c media.steampowered.com/client/installer/steam.deb
$ sudo dpkg -i steam.deb
$ sudo apt-get install -f