The YouTube team had a poster at RecSys descibing their recommender in some detail. The design is intentionally simple, and apparently entirely implemented as a series of MapReduce jobs.
They first compute fixed-length lists of related videos, based in principle on simple co-occurrence counts in a short period i.e. given a video i, the count for a candidate related video j could be the number of users who viewed both i and j within the last 24 hours. The counts are normalised to take into account the relative popularity of different videos, and no doubt massaged in numerous other ways to remove noise and bias. As the paper says, "this is a simplified description".
Precomputed recommendations are cached and served up a few at a time to a user each time they visit the site. Each recommendation is easily associated with an explanation based on its seed video: "recommended because you favorited abc". While this system isn't going to win any best paper prizes it is certainly effective: 60% of all video clicks from the YouTube homepage are for recommendations.