A number of cards exist allowing you to watch and record TV on your PC. Most come with software for Windows only, like so many things, but it is possible to do the same thing on Linux. Linux comes with several drivers which make up the Video4Linux drivers. Several cards are supported by these drivers, and a list of them is available at http://roadrunner.swansea.linux.org.uk/v4l.shtml. This is the driver side. You also need software to use the devices.
Several programs are available to watch TV, capture images and even Web applications. A list of some of the
programs is available at http://www.thp.uni-koeln.de/~rjkm/linux/bttv.html including datasheets.