I have a decoder which can record TV shows. Is recording (copyrighted) TV programs and/or films legal? Is it legal to watch them more than once and back them up on my PC without sharing them with others?
This is allowed under both the Fair Use (USA) and Fair Dealing (Commonwealth) provisions in their laws. Providing the recording is for personal use for the purposes of time shifting then this is fine. Note that personal use does not include inviting all your friends over to binge watch Game of Thrones.
It might vary by jurisdiction, but in general, this is OK -
See the Betamax Ruling clarified that this kind of behaviour falls under fair use - if you want to research it more, look into the law related to "Time Shifting" and "Fair Use" .