It is legal in the United States and United Kingdom to record live TV for personal use. In U.S. law, recording TV programs for later viewing is protected under "Fair Use." It is legal to physically give out copies of TV recordings to other people, but it is illegal to distribute those copies through peer-to-peer file sharing on the Internet.
What You Can Do
You can legally record a broadcast TV program on a recording device such as a Video Cassette Recorder, Digital Video Recorder or computer for your personal use. Recording programming for later viewing is called "Time Shifting" and is a legally supported act. You can view the recorded content as many times as you want, you can make additional copies of the recorded content and you can distribute copies of the content to other people in person. Educational uses of recorded TV content receive additional protection. It is legal to record a TV program and play it for a class.
You can also edit and parody the recorded content as long as the new version adds new value (insight, understanding, aesthetics) to the original. For example, you can parody a music video by changing the audio track to a different song that sarcastically relates to the video's imagery. You also can edit an episode of a TV show to show specific lines a character says to demonstrate that character's attitude toward a topic.
What You Can't Do
You can't hold public exhibitions, rebroadcast, distribute on peer-to-peer networks or sell a TV broadcast recording. Fair use does not protect mass distribution of recorded content or the ability for a person to make a financial profit from a copyrighted recording.
"Fair use is any copying of copyrighted material done for a limited and 'transformative' purpose," according to the Standford University Libraries' copyright law reference. Fair use's primary function involves protecting people's ability to comment and critique copyrighted works. The U.S. Supreme Court ruled that the fair use provisions legally condone people recording live TV programming.
Sony Corp. V. Universal City Studios
The TV recording copyright laws for the U.S. are rooted in the Sony Corporation V. Universal City Studios court case–commonly known as the beta max case. The Supreme Court determined that "video tape recorders" did not infringe on the TV programming copyrights and the potential financial loss to copyright holders from TV recording would be negligible. The case made it legal to produce and sell TV recording devices and for people in the U.S. to record TV programming.