Although you can use your cable or satellite high definition personal video recorder (PVR) to record high definition (HD) content, you can't transfer it to a computer to watch it or burn it to disc.
Currently, there are no Bluray High Definition recorders, like DVD recorders, available in the USA. It is possible with a computer to record live high definition TV shows, movies, and sports. What source you are recording from will decide what equipment you will need.
OTA: Over the Air HD Recording
Over the Air High Definition (OTA HD) content is what you receive with an HDTV antenna that is being broadcast from local television stations. Typically this would be NBC, CBS, ABC, PBS, FOX, etc. For this you will need an Advanced Television Systems Committee (ATSC) HDTV tuner for your computer.