I read a fair number of webcomics, and while the majority of them follow the standard comic format (and thank god for it) and others have a bit of plot in the background, some of them are genuine narratives, simply telling a story one comic at a time. There's a lot of meaty stuff here, but one that I am especially fond of is Ursula Vernon's Digger.
It's the story of a Wombat caught up in the affairs of gods, and while a lot of elements will be familiar to fantasy fans, there are enough tweaks to things to keep it fresh. Some are twists within genre, like oracular slugs, or the title character's engineering bias in a magical world, but some are a step outside those. Most notably, this is technically a "furry" story, in that the main characters include many humanoid animals, but the art is the exact opposite of what you would expect from such an endeavor. Not to put to fine a point on it, there's nary a balloon-breast to be seen. In fact, while the cast is predominantly female, you really wouldn't know that just by looking - they look more like animals than not. Even more, no mention or emphasis is put on the balance of females and it's not a big deal. For me, this is infinitely more delightful than waving a stick around.
But in my emphasis on this meta-stuff, I risk moving away from what really makes it work: Strong characters, solid (sometimes hilarious) dialog and a mythology that really feels like it hangs together well. Digger is a joy to read from the first strip on, and I warn that there's a danger that doing so will eat up most of your day.
As a personal aside, I'm a big fan of Vernon's art in general. Specifically, when my son was born, we bought a large stack of prints of pieces we thought would be well suited to a child's room. The thinking was that we wanted art that would delight a child, but we weren't interested in marketing for Disney. We were delighted with the pieces we got, and I've already started telling Jamie stories about them (though he's still a bit to young to get what's going on).
(That's Vasquez. He's the luckiest bird alive because he pays attention - total nod to Lloyd Alexander there. So far he figures most often in things, though his friend and fellow fez-wearer, Cornelius, is close behind)
Images are, hopefully obviously, copyright Ursula Vernon.