You can bring them in your luggage as long as they are your own personal items. The issues with importing and paying customs duties on them arise when you are ordering them from the US, but having them shipped to you in the UK (i.e. using international delivery on Amazon.com).
However, you should only bring them with you if you will have a DVD/video game player that they will run on. At least for DVD's and video tapes, UK DVD players and VCR's won't play US discs/tapes because they are of a different region (US is region 1, UK is region2)/format (US is NTSC, UK is PAL for video tapes). You can buy multiregional DVD players in the UK which will play any DVD, but if you will only have a region 2 player in the UK, there will be no point in bringing your DVD collection as you won't be able to watch them.