Netflix has a great post on their tech blog describing the energy usage of their infrastructure. They estimate the energy usage and carbon dioxide emissions for their customers when using the Netflix service, not just themselves. They include energy used by TV's home router and cable modems, ISP routing costs, their content delivery network, and their own compute infrastructure. Their comparisons at the end are quite good:

In 2014, Netflix infrastructure generated only 0.5g of CO2e emissions for each hour of streaming. The average human breathing emits about 40g/hour, nearly 100x as much. Sitting still while watching Netflix probably saves more CO2 than Netflix burns.

The amount of carbon equivalent emitted in order to produce a single quarter-pound hamburger can power Netflix infrastructure to enable viewing by 10 member families for an entire year!

A viewer who turned off their TV to read books would consume about 24 books a year in equivalent time, for a carbon footprint around 65kg CO2e - over 200 times more than Netflix streaming servers, while the 100W reading light they might we use would match the consumption of the TV they could have watched instead!