Scott Gatz (Director, My Yahoo) just told me about Yahoo's public beta test of movie recommendations.
Try it out. You rate a few movies, then it recommends movies that might interest you.
Quality of the recommendations seems just okay to me, but this is just a beta, and perhaps things will improve over time. Great to see Yahoo being more aggressive about personalization and recommendations.
It appears that the recommendation engine is provided by ChoiceStream. ChoiceStream uses a content-based algorithm (matching metadata about the movies) that they call "Attributized Bayesian Choice Modeling".
The nice thing about these kind of approaches is that they work well without any ratings data, solving the cold start problem (new movies or when the system doesn't have a lot of users). But, in every implementation I've seen, the quality of the recommendations seems like an issue.
You can also see ChoiceStream's engine running MyBestBets, a recommendation site for TV shows and movies.
Update: A couple months later, this feature has launched.