Ogg Vorbis is an open and patent-free (at least hopefully; several companies have done patent checks on the technology used) lossy audio codec, developed as a replacement for such things as mp3, mp3pro and AAC.
Although hardware Vorbis devices are almost non-existant, the codec is supported by almost all current ripping and/or playback software, and with the advent of version 1.0, released on July 19, 2002 along with a complete specification, it looks likely that it will soon have at least some portable audio player support within a few months. Almost all current versions of audio players support it, such as WinAmp, XMMS, Windows Media Player and iTunes (although the latter two require you to download a seperate plugin, annoyingly enough). Xenex tells me the iTunes vorbis support "is a horrible hack. The files have to have .mov extensions, and there is no tag editing."
It has been developed by the Xiph.Org Foundation, who also provide source code to both a reference encoder (for use in creating the vorbis files) and a decoder (for use in actually playing them), although other groups will be developing compatible decoders (and hopefully encoders, too) based on the provided specification. Note that while the decoder implements the entire specification, the present encoder does not use certain portions of it, meaning that it may improve quite considerably in the future without breaking backward compatibility (and hence compatibility with, for instance, hardware implementations).
Want to start encoding your files to vorbis? If you're on Windows, grab oggdrop and simply drag-and-drop .WAV files to encode them. Otherwise, grab oggenc, a command-line encoder. Also, the majority of free GUI CD ripping applications support vorbis now, EAC and CDex being the two major free Windows CD ripping tools (both of which support it).
The file extension is .ogg; however, don't assume that all files with this extension are vorbis! These files can also include still images, video and text, among many other things; the Ogg file format is a very generic one. Note that Ogg Tarkin and other Xiph.org video codecs use Vorbis for their audio, so the likelihood is that at least the majority of .ogg files will at least contain a vorbis stream (which should play in any vorbis-capable player, albeit without the extra video/image/text content in most cases).
What are the advantages of Vorbis? In a sentence: It's open, with a full specification, there is a full implementation available which means you can use it without having to purchase or write an encoding/decoding engine, there are no patent problems to worry about (no licensing fees!), there is a flexible tagging standard (allowing for custom fields of almost unlimited length), it is generally accepted to provide higher quality at lower bitrates than any other audio codec available and it is slicable ("bitrate peeling", meaning you can simply chop a file up to obtain a lower-bitrate version of it, rather than having to re-encode it, losing quality in the process if you don't have the original file). The last is especially useful for streaming purposes.
Xiph.org have also developed a integer-based decoder (the decoder mentioned above is based on floating-point), for use in embedded applications such as portable audio players. They used to charge a license fee for this, as a source of funding for the rest of xiph.org's activities, however they have recently relicensed it under belowmentioned BSD license. There is currently at least one other (independent) integer-based decoder available, however it is GPLed and as such unusable for many commercial uses, and also incomplete, which may cause it to fail to decode certain files correctly.
The Xiph.org library source code, which is licensed under a BSD-like license (complete with advertising clause) consists of libvorbis, the core library, libvorbisenc, a wrapper library for the encoder portions of the library, and libvorbisfile, a wrapper library intended to simplify manipulation of the streams. Utilities such as oggenc, the encoder, and ogg123, the standard decoder/player, have also been released, under the LGPL license.
It is very simple to integrate into applications, and many programs at least support it, if not use it by default; for instance, modern versions of the Unreal and Serious Sam game engines use it for their audio, as do many new audio tools.