The Rhizome style guide calls for the word "internet" to be written in lower case, but I have been continuing my normal practice of capitalizing it, maverick that I am.
To not capitalize it is more post-internet and cool. It suggests that the internet is not monolithic, but is many things; it suggests that it is an institution (like cinema or television) rather than a technical infrastructure. Heather is convinced that we should continue to not capitalize it.
I feel like capitalizing Internet is more techie and old-school, because in the 1980s there were other proposed "internets" that didn't really take off. So the Internet we use is a proper noun, referring to one possible network of many.
More context: http://en.wikipedia.org/wiki/Capitalization_of_%22Internet%22