It depends. No, really, it depends on the quality of the movie that you're getting.
A faster internet connection will allow us to deliver higher quality videos. But, high quality video streaming will lead to a higher amount of data consumed.
For an entire movie, you'll consume around 150MB to 2GB worth of data. 150MB for a watchable quality delivered to you, and 2GB for the best, greatest, HD version of the movie that you're getting (that you'll only get on a really fast internet connection).
However, to save bandwidth at all times, you can choose to always display lower quality renditions of videos. Learn how to do this here.