Use website-based video downloader, then you don't need to sign up.
Of course! Just go to http://www.youtube-mp3.org/ I use it to get music on my phone ;)
You can find many great tools to help you download videos from Youtube without sign in. For example, video downloader pro. It's a software. Any video that is playing on Firefox, Internet Explorer or another well-known browser can be downloaded with a simple click. If you use the Firefox browser, there is a specific plug-in to get if you want to grab videos from YouTube and other video sharing sites.