Mario Builder's Page on gamejolt.com includes videos and the download for the latest version of Mario Builder. You can also leave comments for the game if you have an account.
Mario Builder's Page on yoyogames.com is where Mario Builder first appeared on the internet. It includes the download for Mario Builder and the option to talk about the game if you have an account.
The Video Game Music Archive is a great website for downloading midi music that you can upload onto Mario Builder.
Mario Builder has a fan page graciously made by Yoyogames user Mario302. The website has a lot of useful stuff which is definitely work a look, including forums.
There is a Mario Wiki which holds tons of information on virtually everything Mario. Although Mario Builder is never going to be perfectly in harmony with the original Mario games, the website is still useful for understanding more about the specific entities of Mario Builder.
Most people have heard of Youtube, probably Internet's best known video archive. Many people have uploaded videos of tutorials and their creations using that website. A simple search of "Mario Builder" reveals this.
Ting_Thing, the author of the Builder, has one other game made called "Stickman's Bad Luck". This is completely unrelated to Mario Builder, but I threw it in anyway.
The Promotional Video for Stickman's Bad Luck...