I recently had a long Facebook wall-to-wall dialogue about this issue. A friend wrote on their status that it is “la internet,” not “el internet.” My argument was that the gender of “internet” (or Internet) depends on the region you live.
This is one of those words similar to computer--el ordenador in Spain, la computadora in Mexico, and el computador in Colombia. According to the Real Academia Española de la Lengua (www.rae.es), “internet” is an ambiguous noun, which means that it can be either feminine or masculine. It can also be written with capital "I" because it is a place or space, just like a country or a city.
Why the confusion?
There not that many words in Spanish that end with "t." Cassette passed into Spanish as "casete" but a very common pronunciation is "caset." Casete is also a noun that can be either feminine or masculine, but in most countries is masculine. By association, “internet” is masculine. Or feminine if “casete” is feminine for you. By the way, “la casete” refers to the cassette player more than the cassette itself.
Speakers who grew up using "la red" (the net) because it is the translation of the English "net," then "internet" logically became "la internet."
Also, "internet" sounds a lot like "carné" (“carnet”) and "bidé" (bidet) which are originally French words and function as masculine nouns in Spanish. This may be another reason why "internet" is masculine for so many native speakers.
New words, specially the ones related to technology, have traveled very fast from English to other languages in the last two decades. Each region adopts the version or translation that it feels more comfortable with. Do not feel bad if somebody tells you, “se dice el internet” instead of la internet and vice versa. You can always point to the RAE. Of course, the RAE doesn't dictate exactly how a region should use a new word, on the contrary, the RAE can include in its official dictionary all the different ways a word is used.
Go ahead, have fun in la or el internet, or Internet.