Like others have said there are several factors that will impact how much data is used from one's broadband provider when using the Roku. The speed of your broadband connection will determine if you are capable of receiving HD streams or only SD streams. The content you view on the Roku could be in either HD or SD format which will impact data rates. If you use more than one Roku at the same time will affect your data rates. And your general web surfing and software/media downloading outside of Roku use will impact data rate usage. Every one's rates will be different.
Most broadband providers now provide ways to monitor or review your data usages now that they are instituting data caps. With AT&T DSL my caps are 150 GB. AT&T does offer a calculator to estimate how much data you might use per month along with a way to see your exact usage on a per month basis. http://www.att.com/esupport/internet/usage.jsp
So far this month billing cycle, using one Roku 2 XS on a 3 mb DSL line (SD content), watching several hours (4 to 6 hours) of content per day/night, mostly Netflix TV shows and a couple of movies along with my normal web surfing, I've used roughly 17.06 GB's of data with 17 days still left in the bill cycle. As my Roku was a Christmas gift this year, my data usage the billing cycle before using the Roku was 7.4 GB, the first billing cycle with the Roku use was 48.5 GB's.
As others have indicated if using the USB Media Player channel or one of the channels, for accessing locally stored media content on your local network, like Plex or Roksbox you will not incur data usage via your broadband provider. Its also possible with the right home theater PC setup and media center software to record over the air digital TV, trans-code it, and have Roku access and play it, again this won't impact the data rate with your broadband provider.