Audacity is a cross-platform multitrack audio editor. It allows you to record sounds directly or to import Ogg, WAV, AIFF, AU, IRCAM, or MP3 files. It features a few simple effects, all of the editing features you should need, and unlimited undo. The audio I/O uses PortAudio, which fully supports OSS, Mac OS X CoreAudio, and Windows WMME, and can be compiled with support for ALSA and Jack.
Developers, don't forget about libsndfile and portaudio
I'd like to point out two other libraries that also deserve mentioning:
1. libsndfile (http://freshmeat.net/projects/libsndfile/), like Michael Pruett's audio file library aka libaudiofile, is a cross-platform library for reading and writing common sound file formats, written by Erik de Castro Lopo. However, while libaudiofile supports just AIFF, WAV, AU, and IRCAM, libsndfile supports all of these plus Amiga IFF, Ensoniq PARIS, NIST/Sphere, and more, plus it supports floating-point samples in the file types that allow it. I've found it to be easy to use and rock-solid stable. If you're writing an application that needs to read or write audio files, look no further.
2. PortAudio (http://www.portaudio.com) is a cross-platform library for doing audio I/O. Rather than writing your application to depend on OSS, ALSA, or aRts, write it based on PortAudio - that lets your users decide which drivers they want to use. PortAudio is also critical for truly cross-platform audio applications, because it supports not only Linux/OSS currently, but also two Windows drivers (WMME and DirectSound), two Mac drivers (OS 9 and OS X), and the Steinberg ASIO driver (used for high-end sound cards on Windows and Mac). Ports for BeOS, Linux/ALSA, SGI, and KDE/aRts are under development.