Video grabbing has been available for many years now. There are quite a number of websites that allows you to grab and download videos into your PC. You key in the url of the video and those websites will do the rest for you.
AllTube Grabber (ATG) does just that on Windows Phone. If you receive a video link from friends in Facebook or email, just copy the link into ATG mini browser address box, click on grab, select the video quality and the video is on the way to your phone.
ATG supports four major video websites. You can organize the downloaded videos into playlist and arrange the video playback sequence. You can also upload them to your OneDrive account allowing you to play the video from any other devices.
Download AllTube Grabber here