I would always use "on".
At least if you are talking about the contents you can find on it.
If you're talking about its hardware structure for instance, then, "in" can maybe fit in some cases, I guess.
english.stackexchange.com/users/1317/Pierre Watelet
I suppose the large number of "in" prepositions in the phrase can be explained like this: in many languages, including Russian we use the preposition which can be translated into English as "in".
So what people often do when they don't know what the correct way is - they "copy" exactly as it's told in their native language.
I guess the number of native speakers who use the Internet is much smaller.
english.stackexchange.com/users/4676/Valentina
'On the internet' would refer to data/items/websites that one can find there.
as Pierre said, the 'Internet' can also be seen as a web of hardware elements like routers and switches.
that switch is 'in the internet'
english.stackexchange.com/users/1848/Stefanvds
If you're talking about information retrieved from the Internet, people routinely say "it is stored ON the Internet", "I found it ON the Internet", "information ON the Internet is ..." etc.
The only example I can think of where you would use "in" would be a phrase like, "I am interested in the Internet".
As noted in response to AmiroucheDouda's post, you might use "in" when "Internet" is used as an adjective to modify some other word.
Like, "We live in the Internet age", "In an Internet-based system, access is ...", "Thinking in Internet terms ...", etc.
english.stackexchange.com/users/13140/Jay
As in this other thread I would use "in the internet" in the context of Application Programming Interfaces, or APIs.
While an Average Joe user reads content off the "front" of an internet website (its Graphical User Interface, or GUI), a function call to an API actually sends a programming thread into the content of the website to retrieve the answer.
That retrieval lends a sense of depth, of looking something up in a website, that reading content that's already displayed on the front just doesn't.
english.stackexchange.com/users/24443/rsegal
When should I use "in the Internet" and when "on the Internet"?
"In the Internet" vs. "on the Internet"
english.stackexchange.com
<word-choice><prepositions><internet><in-on>
english.stackexchange.com/questions/4419
english.stackexchange.com/users/108/bootleg
Generally, most people would use the preposition "on" when referring to the internet. However, if you're discussing its hardware structure, "in" can maybe be acceptable. "In" can also be used when "internet" is a modifying adjective. On the internet refers to data/items and websites that can be found online.The use of "in the internet" would be in phrases like "interested in the internet" or related to Application Programming Interfaces.The use of "in the internet" would be in phrases like "interested in the internet" or related to Application Programming Interfaces.
Generally, most people would use the preposition "on" when referring to the internet. However, if you're discussing its hardware structure, "in" can maybe be acceptable. "In" can also be used when "internet" is a modifying adjective. On the internet' would refer to data/items/websites that one can find there. If you're talking about information retrieved from the Internet, people routinely say "it is stored ON the Internet". The only example I can think of where you would use "in" would be a phrase like, "I am interested in the Internet".  
"On the Internet" is widely used. However, "in" may be used when "Internet" is used to modify another word, or when talking about hardware structures. Generally, most people would use the preposition "on" when referring to the internet. However, it might be acceptable to use the preposition "in" when discussing the hardware of the internet or when "internet" is a modifying adjective in the sentence.
"On the internet" refers to data/items and websites that can be found online. The use of "in the internet" would be in phrases like "interested in the internet" or related to Application Programming Interfaces.
On the internet' would refer to data/items/websites that one can find there. If you're talking about information retrieved from the Internet, people routinely say "it is stored ON the Internet", "I found it ON the Internet", "information ON the Internet is ..." etc.   The only example I can think of where you would use "in" would be a phrase like, "I am interested in the Internet".  
Generally, most people would use the preposition "on" when referring to the internet. You might use the preposition "in" in relation to the internet when discussing hardware or if "internet" is a modifying adjective in the sentence.