Netflix is a great service, it's a shame they don't seem to provide any APIs. Oh, well, we'll have to resort to other means of extracting data.
A little javascript to count how many movies you've rented:
document .getElementById('returned_movies') .getElementsByTagName('tbody')[0] .getElementsByTagName('tr') .length
You can put this code in a bookmarklet or simply type in the Firebug console.
As people say "your markup is your API".