LinuxLinks has a nice list of what they call the Best Free Linux Software. It provides an index that links to a more complete description. Most are available in the Medibuntu repositories. Note that this area is fraught with proprietary software, copyright restrictions, and licensing hassles. In Windows, even recording off-air can get you recordings you can not put on DVD or play on other machines. With Linux, many just bypass these content protection schemes and the warnings and cautions that are often provided with the Linux software.
Some of the LinuxLinks mentions are:
MPlayer, Ogle, VLC, and xine as players for video content. MythTV is perhaps the most complex and complete video recorders and three others are mentioned. Avidemux is a video editor that makes it easy to remove commercials and otherwise tweak your video files. DeVeDe is a very nice way to prepare a DVD from video files.
One category of software that isn’t included is that of DVD rippers. K9Copy is a good example.
You don’t have to spend a lot of money to build your own video library the way you want it. Your biggest problem is probably going to be figuring out what works best for you and how to get the most out of it.