A statistically rough (one sigma) estimate might be 75-100 million servers @ ~350-550 watts each.. Call it Forty Billion Watts or ~ 40 GW. Since silicon logic runs at three volts or so, and an Ampere is some ten to the eighteenth electrons a second, if the average chip runs at a Gigaherz, straightforward calculation reveals that some 50 grams of electrons in motion make up the Internet.
Applying the unreasonable power of dimensional analysis to the small tonnage of silicon involved yields much the same result. As of today, cyberspace weighs less than two ounces. It's hard to gauge its heft more exactly, since devices vary in speed, but to get a handle on The Whole Web instead of just the suburbs we're wired to, try tripling that figure-there are maybe ten times more mostly idle CPU chips in PC's than servers, and fewer very busy ones in the world's comparative handful of supercomputers.