Asus refers to the Linux running on its Eee line of computers as "Linux GPL." Wikipedia has this to say about the Linux operating system running on the Asus Eee:
The installed version of Xandros is tab based; the full desktop version (or "Advanced Mode") may be installed -- but not always easily -- through a set of administrative command prompts. The full desktop version features a KDE 3 desktop with a few modifications performed by Xandros. This desktop mode also provides access to the Synaptic Package Manager which can be used to update and manage the Eee PC's software.
(For more on Advanced Mode, take a look at these items [eeeuser.com].)
Xandros is produced byXandros Corp, which launched in 2001 by Linux Global Partners who had bought Corel Linux after Corel gave up on trying to market its own Linux -- which featured a Wine version of WordPerfect. Corel Linux was based on the Debian distribution. (Other varients of Linux based on Debian include Ubuntu, Knoppix, and Linspire.
An excellent source of tips on modifying the Eee's Linux OS can be read on the forums and Wiki pages of EeeUser.com.
PS: For the full list of apps that are included with the Eee, see this items that lists over 800 of them: wiki.eeeuser.com/dpkg-l