Compiled by Valentin Spirik:
Audacity http://audacity.sourceforge.net/ is an open-source audio editor, available for all major platforms. (*)
Ardour http://www.ardour.org/ "is a digital audio workstation. You can use it to record, edit and mix multi-track audio. ... If you've been looking for a tool similar to ProTools, Nuendo, Cubase SX, Digital Performer, Samplitude or Sequoia, you might have found it." For Linux and OS X (no Windows version), source code available.
Inkscape http://www.inkscape.org/ is an open-source vector graphics editor, available for all major platforms.
The Gimp http://www.gimp.org/ is an open-source image manipulation programme, available for all major platforms. To make the transition easier for Photoshop users there is also the GimpShop http://plasticbugs.com/?page_id=294.
CinePaint (Film Gimp) http://www.cinepaint.org/ is an open-source programme for deep paint manipulation and image processing (e.g. motion picture frame-by-frame retouching). An upcoming update is expected to support all major platforms.
ffmpegX http://www.ffmpegx.com/ is a popular shareware programme for transcoding video on the Mac, maybe not a tool that is easy to use, but works well once configured to one's needs. (The open-source VLC media player http://www.videolan.org/ can also be used for transcoding video and is available for all major platforms.)
Jashaka http://www.jahshaka.org/ is "the worlds first OpenSource Realtime Editing and Effects System", available for all major platforms.
LiVES http://lives.sourceforge.net/ is "a Free, Open Source video editor *and* a VJ tool." It is "fully cross platform for Linux and many flavours of Unix (e.g. BSD, openMosix, IRIX, OSX/Darwin)."
Kdenlive http://kdenlive.org/ is "a non linear video editor for the KDE environment running on Linux. It is based on the MLT video framework which relies on the FFMPEG project".
Ubuntu Studio http://ubuntustudio.org/ is "A multimedia creation flavor of Ubuntu" and "aimed at the GNU/Linux audio, video and graphic enthusiast as well as professional. We provide a suite of the best open-source applications available for multimedia creation. Completely free to use, modify and redistribute. Your only limitation is your imagination."
Blender http://www.blender.org/ is an open-source 3D modeling/animation programme, available for all major platforms.
See also the Wikipedia iMovie and Windows Movie Maker entries for basic (commercial) video editing software (en.wikipedia.org). A basic DV video editing software for Linux is the open-source Kino (www.kinodv.org).
(*) Mac OS X Audacity bug: if you hear no sound when watching .flv videos (e.g. YouTube) after using Audacity: Open Audio MIDI Setup (/Applications/Utilities/) and change the "Audio Output setting" from "96000.0Hz" back to "44100.0Hz" (see also Mac OS X: No audio from certain multimedia content). (docs.info.apple.com)