I\'ve always been curious as to how these systems work. For example, how do netflix or Amazon determine what recommendations to make based on past purchases and/or ratings?
This is such a commercially important application that Netflix introduced a $1 million prize for improving their recommendations by 10%.
After a couple of years people are getting close (I think they're up around 9% now) but it's hard for many, many reasons. Probably the biggest factor or the biggest initial improvement in the Netflix Prize was the use of a statistical technique called singular value decomposition.
I highly recommend you read If You Liked This, You’re Sure to Love That for an in-depth discussion of the Netflix Prize in particular and recommendation systems in general.
Basically though the principle of Amazon and so on is the same: they look for patterns. If someone bought the Star Wars Trilogy well there's a better than even chance they like Buffy the Vampire Slayer more than the average customer (purely made up example).