The Google Video Blog announced the launch of “Personalized Video Recommendations” feature that show multiple videos that pertain to your search interests, underneath the hot videos section of the homepage. You can click on the arrow buttons in the top right corner to see more recommended videos. Google uses your past search queries and videos that you've watched to suggest personalized videos.
To see personalized videos, log into your Google account and visit Google Video. To take advantage of this feature, you'll be asked to sign in to Web History. It's up to you how much customization you'd like - for example, you can choose which searches are included, and which aren't.