I have had an idea for a site, its basically embedding youtube videos and would be a directory for the topic, the name I have thought of is shownametube.com and was just wondering if generally this is allowed? Both having a site full of youtube videos and using the "tube" name.
You'll need to read Youtube ToS very carefully. If I remember correctly you aren't allowed to embed their videos on commercial sites (having any form of advertisements would be seen as commercial). You'll also need to ensure that the videos you embed don't contain copyrighted content otherwise you could be held responsible for contributory copyright infringement.