I always thought that you were supposed to capitalize proper nouns. And to me “Internet” is the name of a unique thing (as is Web). There is only one Internet and one Web so they deserve the caps. With all due respect to Wired and Zeldman, until we have more than one Internet or Web, I think the capitals remain.
Referring to a “Web designer” or an “Internet consultant” doesn’t allow you do drop the under the argument that there are many of those. The Web and Internet in those terms are adjectives modifying the nouns and as such (I believe) retain their caps. Just like “Pope watcher” or “Madonna fan” aren’t “pope watcher” and “madonna fan”.
BTW, I use e-mail, not E-mail, intranet, not Intranet (there are lots of intranets, not just one), and Net (short for Internet) not ‘Net or net.