Is Youtube banning conservative videos without cause?
There's a discussion of that here, including two videos side-by-side: one from the rightwing side that was deleted by Youtube, and an apparently similar one from the other side that was not. I haven't looked into it, but there are also a series of videos here, some of which may have been deleted by Youtube.
On the mitigating side, I believe that widely-watched Youtube vlogger "sxephil" was complaining about one of his videos being deleted and that was apparently because he said a bad word or something. Thankfully, I didn't bother watching that.
There might be a reasonable explanation, or it might be that "liberals" are flagging videos with which they disagree rather than appreciating an open debate, or it might be just Youtube showing their stripes. I'll leave it to you to look into this topic and provide examples of videos that were unjustly deleted.
Note that back in December 2007, CNN and/or Youtube censored two of my video replies on the raw CNN debate footage, leaving replies that didn't point out how bad CNN was in place.
UPDATE: This says that the account belonging to someone who'd uploaded a BBC WTC7 video was cancelled, despite the video having received a million views. The same video is apparently available elsewhere on Youtube, and what caused the problem isn't known but is presumably because of a copyright complaint from the BBC. The solution to problems like this is to document everything and also only upload things that clearly fall under fair use.