Kideo player: curated YouTube for kids
I have to admit, it totally won me over.
Kideo Player is curated by a father of two, and his taste is videos is a lot better than the spotty results you get from community moderation. The curator has a stake in the videos he selects, because his own kids watch them. Minimizing parental annoyance seems to be a priority, too: think Sesame Street, not nightmarish gummi bear. The library of videos seems to lean heavily toward educational material: I saw sign language, Spanish lessons, and animal vids when I was watching.
Kideo Player also has a more attractive, more kid-friendly design than Totlol (the dog and cat mascots are seriously adorable), and controls that even a two-year old can use by himself. Hitting spacebar skips to the next video. That's the only thing a kid has to learn to use the site. All in all, this is exactly the video site I would have wanted if YouTube had been around when I was a little kid, and probably the site my parents would have wanted, too.