As others pointed out only about 1 in 1000 are posting reviews on Amazon so they aren't doing anything particularly great, they just have volume.
I will share one trick that I use on my site UniversityTutor.com, to get more reviews. I saw this in an email that Google Checkout sent out:
1. Firstly, of course you should send an email asking the person to leave a review a week or two later
2. Do NOT require the person to login to leave the review (use a "one time login link"). Removing this hurdle can help.
3. Embed the actual review form RIGHT IN the email. With a submit button.
Basically all this is about reducing the hurdle to leaving a review as much as possible. The "archive" button is just to easy so if they have to leave the email or login you've already lost people.
Submitting forms doesn't work in all email clients so you'll have to also include the one time login link for anyone who can't submit the form right from their email. But it does work much of the time. To generate the HTML for the email form that works across most email clients, the easiest way I've found is to create a new form in Google Docs, and email it to yourself as a starting point to copy from. The HTML they generate is pretty well optimized from what I've seen.
I still don't have tons of reviews on that site though. So it is definitely tough to get people to engage.
Also - the simpler the review the better.
A pulldown will get filled out more often than a free form text field.
Radio buttons will get filled out more than a pulldown.
A simple thumbs up thumbs down will get filled out more often than 5 stars.
And only a thumbs up (or like) will get more than thumbs up or down.
When I moved from a 5 star thing to just up/down on BuyersVote.com it helped a bit with engagement.