I have, for a long time, and for many of the reasons Joseph Turrow suggests, thought that capitalization is unnecessary. It is, after all, a part of everyday life. Moreover, capitalization implies something unitary and definite–the internet (despite the “the”) is neither. So, if you look at my masters thesis and Ph.D. dissertation, you will find the lower-case “i” throughout. In things I’ve written in the interim, I have been forced by house style guides to use the capital “I” (with the exception of New Media & Society, which has used the lower case from its inception).
The question not addressed is whether it is “Net” or “net,” and whether it is “Web” or “web.” In both cases, but especially the former, the possibility of ambiguity is introduced. Nonetheless, I prefer the way the text looks when web and net are left lower-case.