There are many methods and reasons behind capturing footage. You may want to make a movie using Matinee or you want an animated level preview. Either way there are different programs to use which help the process.
Fraps is a program orginally designed to display your framerate in all OpenGL and DirectX games. It also has the ability to capture the output of any of these games and write them to an avi file. Unfortunately the output file is huge and will no doubt need to be compressed. I would recommend the latest version of DivX. Finally for editing of the avi file you'll probably want to use a program such as Virtual Dub. Fraps does not capture sound at all. OpenGL is the recommended mode of capture for Fraps version 1.9a and below. For 1.9b and above, Geforce users will see DirectX is also recommended along with OpenGL.
ShortCutMan: Just a small note, Fraps is in version 2.0 now, and can capture sound with the movie. But
you now have to pay if you want to take for than 30 seconds of video. Its $29.95US.
Runs from the command prompt, starts UT with a particular map and outputs a huge stream of BMP or JPEG files at a set framerate.
Unreal Movie Studio is a Matinee style Gametype for Unreal Tournament. This is not availble in UT2003. Maps must be edited and have their Gametype set to a special type defined by this package. Not video capture per se but rather planned, scripted ingame demos. Fully controlled cinematics for single player campaigns or even stand alone movies can be made using the studio, and tutorials are available from the UMS site. See UMS.