The web, not to mention my email inbox too, is awash with programs that claim to be able to download Youtube videos and convert them to various formats for offline watching and viewing. In my experience, though, most of them don't work too well, and aren't worth the trouble of downloading.
So, for a change, here's one that's actually rather good.
It's called Freemake Video Downloader. You can get it from http://www.freemake.com/free_video_downloader. It works on Windows XP and above and the download is a 1.2 MB file (although be aware that it'll download another 12 MB during installation).
The offline setup of the program can be downloaded from this link :
VirusTotal reckons that the program is free from malware and viruses. However, be aware that it uses the OpenCandy system, which means that it will offer to install one or 2 additional programs for you. Pay attention during the installation process, and simply tick the "no" boxes unless you want those extra offerings.
Once installed, using Freemake is very simple indeed. When you access Youtube in your web browser, a new "Download" button appears above the video you're watching. Press the button and Freemake springs into action, and displays the options shown in the screen shot below. Choose your desired output format, press the Convert button, and you're done. Not only can you download videos in this way, but you can also extract the audio in MP3 format so you can listen offline.