A lot - although exactly how much is still not clear. The question is becoming a hot topic, not least thanks to a Guardian report in which senior officials voiced concerns over the growing financial and environmental cost of powering vast internet data centres as it expands.
But the energy footprint of the entire internet is much more than data centres - it includes the devices we consume the internet on (computers, mobile phones, iPods and more) as well as the telephone exchanges that deliver information.
Given this wide variety of places where energy is spent, there are few clear-cut studies that show how much the internet as a whole consumes. The lack of clarity has caused confusion and irked some industry bigwigs, in particular Google. The company's latest word on the subject came in a post on Google's official blog, where Urs Hölzle - the internet giant's senior vice-president of operations - took pains to point out (again) that the energy cost of conducting an online search was very small, producing 0.2g of carbon per search.
Hölzle also suggested that the efficiencies afforded by networking technologies - faster communications, fewer trips made by car, more productive working - far outweigh the energy footprint of the internet itself. "After all," he wrote, "It's much more efficient to move electrons than to move atoms. 'Virtual' tools such as email, video-conferencing and search engines replace more carbon-intensive activities such as snail mail, business travel, and driving."
Is that accurate? Possibly. Data on the potential energy savings that could be produced by hi-tech systems is patchy, with the clearest possible outline published in a report released last summer by the Climate Group, which consists of 40 corporations and numerous local and national governments. The paper - which focuses on CO2, not energy - suggests that, by 2020, the internet's footprint will have tripled to 1.43bn tonnes of carbon emitted per year, largely thanks to increasing use of PCs and mobile phones, and driven by exploding economies such as China and India. However, it also suggests that improvements made possible by information technology - such as smart logistics, energy-aware buildings and more efficient energy grids - could reduce emissions by 15% overall.
However, those savings are contingent on a host of new systems being used in businesses, homes and products around the world. Trumpeting such benefits is something energy experts have expressed scepticism about, although they agree that if such change is achieved, the benefits could be significant.
Perhaps the place to start is in making the numbers more clear. The inventor Saul Griffith certainly believes so. "Galileo said, 'measure what it measurable and make measurable what is unmeasurable'," he told the Guardian. "Part of the reason humanity is in the situation it is with climate change is that we weren't measuring how we were using energy and understanding the consequences."