A software application which handles the editing of video sequences on a computer is called video editing suite (software). It can also manage limited editing of the audio clips which accompany the video or at least the ability to sync the audio with the video.Image editing applications like vector graphic software typically show one image on a large area on the screen and a view of the directory. To hold many files in the directory, it is possible to zoom out, so that a single file only covers one pixel-line in the editor, or even less, for rough cutting. A play button lets the software automatically advance to the next image, thus playing the video. Like slide show editing software that comes with a lot of image file format decoders, video editing software comes with plenty of video codecs.
Some of the best video editing software are quite expensive, like Adobe Premiere and Apple's Final Cut Pro. However, thanks to these valuable free and open source video editing software applications, you don’t have to empty your wallet.
Jahshaka
Jahshaka aims to become a cross-platform, open source, free, video editing, effects, and compositing suite. It is currently in alpha stage, supporting realtime effects rendering, but lacking useful implementations of many features such as the non-linear editing system. It is written using Trolltech's Qt, but its user interface is written using an OpenGL library to create GUIs.
Once finished, it would be in the same market space as Newtek's Video Toaster and Pinnacle Liquid Edition. With all promised features it would be a rival to Adobe's After Effects or Autodesk's Combustion - in fact the GUI is heavily based upon Combustion.
Since it uses OpenGL and OpenML, it could be ported to many different platforms; theoretically, it should run on any platform that supports OpenGL and has the necessary computing power.

Avidemux
Avidemux is a multi-purpose video editing and processing program. It is written in C/C++, using the GTK+ graphics toolkit, and therefore is truly a platform independent, universal video processing program. It is available for almost all distributions of Linux that are capable of compiling C/C++, GTK+ and the SpiderMonkey ECMAScript scripting engine. A Win32 version of this program is also available for Windows users, as well as Mac OS X, FreeBSD, NetBSD and OpenBSD ports and packages. The program has also been successfully run under Solaris, though no official packages or binaries exist for it. The program can be run in 64bit operating systems that are non-Windows and non-Macintosh based.

Cinelerra
Cinelerra is a free and open source software non-linear video editing system. It is designed for the Linux operating system, but has also been successfully ported to Mac OS X. It is produced by Heroine Virtual, and is distributed under the GNU General Public License. Cinelerra also includes a video compositing engine, allowing the user to perform common compositing operations such as keying and mattes.
Cinelerra was first released August 1, 2002, and was based in part on an earlier product known as Broadcast 2000. Broadcast 2000 was withdrawn by Heroine Virtual in September 2001.
As a professional editing program, Cinelerra requires significant computing power.

Kino
Kino is a free software, GTK+-based non-linear digital video editor. Its vision is: "Easy and reliable DV editing for the Linux desktop with export to many usable formats." The program supports many basic video editing and assembling tasks.
Kino can import raw AVI and DV files, as well as capture footage from digital camcorders using the raw1394 and dv1394 libraries, and export to camcorders using the ieee1394 or video1394 libraries. Kino does not support Linux 2.6.22's new firewire stack.
Kino is included in the public package respositories of several GNU/Linux distributions, including Debian. BSD ports are also available.

LiVES
LiVES mixes realtime video performance and non-linear editing in one application. It will let you start editing and making video right away, without having to worry about formats, frame sizes, or framerates. It is a very flexible tool which can be used by both VJ's and video editors - mix and switch clips from the keyboard, trim and edit your clips, and bring them together using the multitrack timeline. You can even record your performance in real time, and then edit it further or render it straight away as a new clip !
For the more technically minded, the application can be controlled remotely or scripted for use as a video server. And it supports all of the latest free standards.
LiVES is good enough to be used as a VJ tool for professional performances, and as a video editor is capable of creating dazzling clips in a wide variety of formats.

I have written an editorial about the sad state of HOME video editing under Linux, and two lead developers of applications you actually link here, agree with this. In fact, I had lunch with one of them this afternoon (no, I am not playing with you).
I'd love to see a GOOD video editor on Linux, but right now, none of them do what most home users expect to. And they are all extremely bad performance and stability wise with HDV, while they don't support AVCHD *at all*.
Further reading:
http://eugenia.gnomefiles.org/2008/01/20/video-editor-mockup/
http://eugenia.gnomefiles.org/2007/12/03/the-linux-video-editor-situation/
It's called Saya-VE (recursive acronym for "Saya-VE ain't yet another Video Editor" :) ). The project was just started 3 months ago and we're currently recruiting C++ developers.
The main difference with other video editors, is that I've set up the following priorities:
1. Ease of installation (no linux dependency hell / hard to install libraries)
2. Solid, extensible architecture (plugin-based; no spaghetti code that crashes everytime you move the mouse)
3. Support for a wide variety of file formats and codecs (through the use of GStreamer - don't worry, we're working on embedding a separate copy so you don't have to worry about installation/configuration blues )
4. Well-thought, user-friendly interface ( we have TWO usability Nazis in the team experts in Adobe Premiere and Sony Vegas, so we're serious about that!)
5. Cross-platform compatibility (and that includes Microsoft Windows(TM)!)
We can make this happen! C++ Programmers, unite!
Saya Video Editor homepage
Saya Video Editor Official Blog
I agree with Eugenia that a lot of the tools mentioned do fall a little short of the ideal requirements (as defined by the industry leaders such as Final Cut Pro and Adobe Premier). But I do think that they should be applauded for giving the average consumer a free alternative to those expensive products. In addition to that I believe that the Cinelerra product is actually quite full featured and capable, although it does require lots of computing power as stated in the article.
Rick - I am very interested to read about your full featured editing tool and will be checking out your site with a view to, perhaps, adding some information about the product to free-video-editing.com.
The "hardest" part right now is getting a c++ thread library.
When I get this done, the core will be complete and i'll start implementing plugins for reading video / audio.
Subscribe to my blog's feed, and you'll get all the details on further advances.
http://www.kdenlive.org/
Professionals isnt who were are looking to cater to.
First you learn to walk, then you think about doing the 100m in the Olympics.
My friend swears by Blender which he tells me is a world class software in its field (too high a learning curve for me) but its overkill as are Final Cut and other such programs for 99.9% of people.
I want to be able to do basic editing like taking the videos from my digital camera and putting them together and it works with with various programs.
What we have to do is make them more intuitive and easy to use for the non pros.
Take the top 10 functions that real people use in video editors and make them as easy to use as possible with as little steps as possible.
I hope one day that other free software programs will have Blender's reputation of excellence but let's face it, those programs are not for most people.
We have to think about dummifying programs like Garageband which are nice toys that serve the majority of users.
The real musicians will get real programs when they have to but for the majority of people on Macs it does the job.
Talking about Final Cut when talking about these expensive programs is setting yourself for
yourself for disappointment.
Good luck to Saya-VE crew.
I've followed Jahshaka vaporware for years now ("once finished... promised features..." same thing year after year.) I use Blender for 3D and I've tried to deal with it's bizarre UI for video editing too. Ugh. I've faithfully contributed bug reports on Kdenlive. I've dealt with the vagaries of Avidemux, ffmpeg, mencoder, and the rest. Good utilities for certain purposes like transcoding , sure. And I can deal with running Photoshop and Sketchup in a VM or Wine on a couple of other programs - but video apps just don't work with those methods.
I've recently gone back to dual booting Ubuntu and Windows, so I can use the new v. of Premiere Elements 7, a wonderful little $100 program that does it all and, I hate to say it, beats all of these FOSS programs up down and sideways. Sorry but I will pay for software when open source drops the ball so thoroughly and consistently.
I sit back and watch the developers of Ubuntu, for instance, all this effort and work, every six months with a new OS release. The OS is fine. The OS is not the problem. Stop it already. Stop moving around menu items in Gnome. Stop all development of the OS and put those people on the Kdenlive team, on the Lumiere team, on the Gimp team, on the Inkscape team, and in six months or a year we could shape these nice little apps up into actual true killer apps. And this would finally allow a whole host of people to finally use Ubuntu and Linux without apology and without feeling like the ugly stepsister with her legs cut off.
I also had a go at AVIDMux but had to give up. I am not a computer geek or wizzard and found the user interface very user unfriendly and not intuitive at all. Although people keep saying that there are lots of tutorials available, I have yet to locate those that really help newbies. In addition, it kept crashing all the time on Windows 7. Unfortunately, I couldn't find any information on how to get around that.
Kapadokya