In US publications, Internet is usually capitalized. The argument is that it is a proper noun (like Rome or Richard or Ritz Crackers), and thus it should follow the capitalization rules for proper nouns and have the first letter capitalized. (Note, however, that web and website are not capitalized, but World Wide Web is.)
I can almost agree with this thinking. In a way, the Internet is sort of a place (and proper nouns are the official names for people, places, and things), but it comes to you instead of you visiting it, as you would, say, Texas. You can’t go to a server, touch the box, and say, “Hey! I’m at the Internet! I should get a post card for Grandma!”
I’m more aligned with the prominent UK style, which is to leave it lowercased. It’s not a brand name, and brand names get capitalized. And it’s not really a place, not like Texas or Rome. When I think of the Internet, I think of it as a technology. We don’t capitalize general names of technologies; think about radio or television. Why should the Internet be different?
As a US-based book editor, I’m a slave to style. So, I capitalize Internet. But I’m hoping we move away from the capitalization soon. To me, it doesn’t make sense.
What do you think? Let me know in the comments section.