I glossed over this briefly in the Screenshot thread (http://forums.spheredev.org/index.php/topic,6.msg1659.html#msg1659), for those who would like to record their session in one of the Sphere engines or one of the editors, you have a few options available to you:
Wikipedia has a more complete list of video editing programs (http://en.wikipedia.org/wiki/List_of_video_editing_software) than presented here for the three major operating systems, and a list of video screen capture programs (http://en.wikipedia.org/wiki/Comparison_of_screencasting_software).
Free video capture programs include CamStudio (http://camstudio.org/), HyperCam (http://www.hyperionics.com/hc/), and .kkapture (https://github.com/rygorous/kkapture) (alternate URL (http://www.farb-rausch.de/~fg/kkapture/)), among others. TechSmith, maker of the commercial Camtasia, also has a free app Jing (http://www.techsmith.com/jing.html) for capturing as well but is limited to 5 mins at a time (not a problem for the preview video). Another free, open-source capture solution on Windows is the recently released Open Broadcaster Software/OBS (http://obsproject.com/).
TechSmith Camtasia Studio is so far the leading commercial video screen capture available and is available on Windows and Mac OS X. Fraps is another commercial capture solution of lower cost than Camtasia but known to be buggier and prone to significantly lowering the performance of the thing it's trying to capture.
Linux-specific video capture programs include Kazam and SimpleScreenRecorder (http://www.maartenbaert.be/simplescreenrecorder/). A third capture program, RecordMyDesktop, is also available but is reported to have critical bugs that prevent it from being a long-term recording solution.
Linux-specific video editing programs include LiVES (http://lives.sourceforge.net/), Kdenlive (http://www.kdenlive.org/), and Cinelerra (http://www.heroinewarrior.com/cinelerra.php) ("community version" (http://cinelerra.org/)).
Mac OS X
QuickTime Player (possibly QuickTime X) can reportedly perform video capture of the screen. I don't know if it requires a Pro license, however.
TechSmith Camtasia Studio, as mentioned above, is commercial and is available on Window and Mac OS X. Jing also has a Mac OS X version with the same limitations as its Windows counterpart.
Free cross-platform video editors apparently include Avidemux (http://avidemux.sourceforge.net/), Jahshaka/CineFX (http://www.jahshaka.com/), the not-yet-stable VLMC (http://www.vlmc.org/), and OpenShot (see below). Nothing specifically Mac is available for free.
If you have nothing else, use FFmpeg (possibly with a GUI front-end like WinFF) to convert to the chosen formats if needed. You may also use FFmpeg for splitting and joining if nothing else is available. FFmpeg is free, open-source, and has Windows, Mac OS X, and Linux versions available. It's primarily command-line, but GUI front-ends are available for each of its systems.
OpenShot (http://www.openshot.org/) is a video editor and is currently Linux-only, but is expected to go multi-platform when version 2.0 is released by the end of 2013 thanks to a successful Kickstarter. Once OpenShot is finally cross-platform, that will likely be the graphical video editor I recommend from then on.
Improving this list
If you have constructive suggestions to add to this list, please feel free to add a reply!
Nice post. I'd like to point out that RecordMyDesktop is not really recommended. It has some weird bugs that make it impractical to use. For example, it has problems with the capture speed, and the file format it exports (ogv) has a misbehaving codec which is not supported well by video editors.
Updated to reflect RecordMyDesktop's bugginess, thanks!
I use OBS (http://obsproject.com/) myself, but it requires DirectX 10 to run at the time of writing.
Added OBS, thanks mezzoEmrys!
Also added Fraps in Windows commercial paragraph.
Okay, I must say... For Linux SimpleScreenRecorder (http://www.maartenbaert.be/simplescreenrecorder/) is just amazing. It can record 1080p HD at 60 FPS in high quality MP4 with around 30-60% CPU usage. This is on a 2 Ghz 4-core i7 system. No other software would do this.
It also comes with a library that, if you use it, hooks straight into OpenGL, which means even better speeds when recording games that use OpenGL. I tried it with 0 A.D. and it works great.
Added link to SimpleScreenRecorder in original post!