With its first edition dating back to early 1995, Matt Welsh's book is widely regarded as classic, to the extent this term can be applied to Linux. Mr. Welsh, now continuing his PhD studies at UC Berkeley, is a renowned Linux expert, and was actively involved in Linux development since 1992. In particular, he is known in the Linux community for starting the Linux Documentation Project, for contributing to it with Linux Installation and Getting Started (LIGS) Guide (available freely from the Internet) and, lately, for being the founding editor of the Linux Magazine.
Running Linux grew out of LIGS as its expanded and professionally edited version. This has its pluses and minuses. When it came out, there were hardly any other books on Linux available, so it tried to teach the reader everything, from Linux installation to Unix administration, from the command shell basics to compiling the kernel, and from using the C compiler to configuration of X Windows. Its breadth is thus encyclopedic, and yet it is surprisingly sharp at details. The third edition added all the things that happened since: KDE, GNOME, Samba... It may be my personal feeling only, but the new chapters somewhat stick out, without really growing into the tissue of the text.
More important, the book fails to recognize that the structure of new Linux users changed since 1995. At the time, it was written as a "getting started" guide, and it served its role perfectly. However, nowadays you cannot assume any more that every new Linux user is familiar with command line commands or other Unix systems. Therefore I don't think I could still recommend Running Linux as a beginners' guide.
Being one of the top-selling books on Linux, it doesn't need any particular recommendation, anyway. Still, Running Linux is a book edited to high O'Reilly standards, and written by some of the most knowledgeable people in Linux community - which is to many a definite plus compared to books written by journalists. I would say its best target population are seasoned Unix users wanting to try Linux, technically minded people in general, and CS students in particular. Others might find its learning curve somewhat steep.