Gunnerkrigg Court, a fantasy webcomic that is strange, mythic, enormous, and funny. I was hooked in the first chapter, when the protagonist, newly-arrived at a very strange school, discovers that the second shadow she has acquired is a creature who needs to cross a very brightly-lit bridge to get home to a forest. But she's not permitted to leave the school grounds. "There was only one sensible resolution to this problem," she decides, which is to tell the shadow:
"I must construct a robotic walking device which will provide you with transit across the bridge!"
Naturally!
This led, as I mentioned in my epic Nexus 7 post, to a glorious and ill-advised binge through the entire archive to date [*], and I like it a whole lot.
(The story of the shadow and the robot turns out, over 40+ chapters to date, to actually be a much more appropriate introduction than I thought, but one of the things I do like about the story is that it takes the time for little side-stories along the way, some of which may connect in later and some of which may not, who knows? I'm not clear on the shape of the story yet or how much there's left, but I definitely get the impression that there is an overall plan.)
tithenai has a likely more useful recommendation post (which also includes praise for Homestuck, but since I can't usefully read that offline, I resist!).
[*] I made an offline archive for my own use and loaded it on the N7. If this would help you read the story, and if you promise to either go click around a lot to give pageviews (the site has ads) or buy swag/donate if you like it, then I will share them with you; drop me a comment/PM.