LiVES is a video editing system, which provides realtime editing and mixing, can apply realtime rendering effects, or just perform format conversions. It's suitable both for newcomers and VJs, available cross-platform, runs even on low-end hardware, and is extensible per RFX plugins.
Ardour is an audio processing and editing application. It integrates broad hardware support, JACK and ALSA backends, flexible recording features, multi-channel nesting, import and exporting various file formats, comes with ready to use samples from freesound.org. It has a pretty editing UI, mixing, routing, monitoring, panning. Ardour allows non-destructive and non-linear editing, can be used for augmenting audio layers in video files even. And comes with many effect, input and output plugins. I
Mixxx is an audio mixing / turntable software for DJs. It provides a dual-deck interface, easy drag and drop. It's GUI has various wave transformation controls, beat and cue points, and full waveform previews, vinyl emulation, sample stretching, single click looping, quad sampler decks, MIDI controls. It also helps organazing playlists, with BPM detection, an auto DJ feature, recording, replaygain normalization, and even ICY broadcasting.