Should the word 'internet' be written with a capital letter? Why?

Internet Explorer is, internet isn't.
The answer is yes, but I'm not sure why.
It depends on how the word should be used, if you are using the word as a noun, then it is a proper noun (such as the noun Britain or France) so it shoudl be written with a capital letter:

The Internet is a global computer communications network.

However, you can also use the word as an adjective, in which case it shouldn't have a capital:

My internet connection is broken.

P.S. No davidjohnsenelwyn, you are wasting your own time.
Why do ppl. give a damn to such trivial things. There are many bigger things to concentrate on.
I think it's normally capitalized because it's a proper noun - a 'place' if you will, like 'Interstate 495'.
Convention dictates that THE INTERNET be in capital letters when refering to the network of computers which bindes the world together. When refering to a network of computers within a company, then it is the company inter(nal)net(work).
My personal viewpoint on this, and it's not official, I don't even know if there is an official English answer is that it should never be capitalized.

The internet was not an entity created on purpose, it sort of organically grew. It is also not a set thing, there is not real official definition, it's these 12 thousand computers that yadda yadda.

I would not, and do not, capitalize it except when it begins a sentence.
I only put it with a capital at the beginning of a sentence, otherwise I think it looks silly: I'm using the Internet
I'm using the internet.

Why would it need a capital letter? It's not a name or anything, as far as I know, it is short for "international network" so uness you are German, it doesn't need a capital because only proper nouns need capitals(like a name of a person, country or company)