Follow up:

It turns out there are several websites out there besides Youtube that put out great videos for not just the general public but kids too. If you are a parent looking for a video website for kids you have come to the right place for such information.
Youtube is a great place to find videos because it has just about any video you can think of. From Cartoons to "howto" videos about Calculus. Its interesting to speculate how many videos actually exist on Youtube. But it turns out that not all videos are suitable for children. I will provide you with some of the results that I have found that are great for kids.

Tinytube

This is one of the nicest looking kid friendly video websites out there.
"TinyTube is your source for all things beneficial to your children. Ranging from movie trailers to educational videos and funny videos, TinyTube has everything your child needs on one site to be entertained for as long as you'd like.

Improve math and reading skills, watch funny animals or simply go through the many kids' movie trailers to come up with that family movie night selection in the future.

TinyTube is child friendly, providing the best videos for children of all ages to learn and to grow along with your help and the videos on TinyTube."
http://www.tinytube.com/

ItsAGoodDay.org

This website started not too long ago. Its aim is to create a "PG Youtube". "All videos are filtered by a human eye. You tube, Stupid Videos, etc all have their rating systems and codes for adult content, but this site will not contain any content up and above a PG rating. The videos will either be accepted or rejected based on the evaluation of this material. We will not edit the videos, but rather they will be rejected. This screening process will delay the immediate viewing of the video, however our users will appreciate the screening time" www.itsagoodday.org

Nick Jr. Video

Nick Jr. had started there own video website in an attempt to create a Youtube clone for kids. On their website you can watch full episodes of your favorite shows. Including many kids favorite; SpongeBob Squarepants.
http://www.nick.com/turbonick/index.jhtml

Related questions to this article.

Where can I find a video website for kids?
Where can I find a family friendly YouTube website?
Where can I find a YouTube for kids?
Is there a video website for kids?