YouTube is an incredible tool for sharing videos and starting conversations with people around the world. Unfortunately, not everyone knows how to have a civilized conversation, and some people take great pleasure from leaving inappropriate comments after YouTube videos.
If you're having problems with the comments folks are making about your YouTube videos, you need to change the comment settings for your video. Go to My Videos and then click on Edit Video for the video that's getting the comments.
Comments are located under Broadcast and Sharing Options and there are various settings to choose from. I recommend letting only YouTube friends comment, or only posting comments after approval.
You can't delete YouTube comments (unless they violate the site's terms), so it's better to play it safe than have an unsavory comment permanently attached to one of your videos.