Amazon doesn't require a purchase to leave a review, but it's worth noting that if have purchased it through Amazon, they'll tag your review with a little "Amazon Confirmed Purchase" badge.
Requiring a purchase through Amazon would drastically cut down on the number of reviews they would get; lots of people own lots of books and movies and albums they purchased before Amazon existed and can give good reviews of them. I don't think it's reasonable to expect Amazon to shut those reviews out.
I meant it as a change for new books coming out, not for, say, your favorite Pink Floyd album. Existing products/reviews should be, for better or for worse, left in place of course.
Part of why Amazon is great is it being a place where you go to research things. I'd hate it if they close reviews to only people who have bought stuff at Amazon - it'll take away too many good reviews.
Requiring a purchase through Amazon would drastically cut down on the number of reviews they would get; lots of people own lots of books and movies and albums they purchased before Amazon existed and can give good reviews of them. I don't think it's reasonable to expect Amazon to shut those reviews out.