I'm a self-confessed webcomics addict. I'll talk about my top three for now, with a capsule description of why I like them, and add more when I remember them. If you have any recommendations, I'm always looking for new stuff to add to the list.
Schlock Mercenary: Science fiction / comedy. It follows the adventures of a group of mercenaries as they try to make a profit, stay one step ahead of a steadily increasing roster of enemies, and get involved in events that seem inconsequential at first but soon escalate to fundamentally change the galaxy. The archives go back almost seven years of daily updates, so there's a lot to read--though the author did put in a "jump in" point more recently if that's too daunting. The art is poor quality at first, but steadily improves as time goes by.
Scary-Go-Round: This one is very hard to sum up. I could describe it as a surreal comedy with a distinctly British flavour, about a group of twenty-something friends in a world gone mad. Or as a soap opera with brilliant characters and drama. Or as a tale of leprechauns, devil bears, time travel teapots, Satanic nuns, embassies from the land of the robots, and the Orkney kraken. But really, it needs to be read to be appreciated. Some of the characters were carried over from an earlier webcomic by the same author, though it is reasonably stand-alone. It's also notable for wildly changing art styles over it's life.
Errant Story: Fantasy. A half-elf sorceress needs something really spectacular to pass her final exams, so decides to look into legends of a spell that will transform her into a goddess and let her rule all of reality. However, this grand scheme runs into trouble when other people begin to take an interest in her quest--a human assassin without a heart of gold, and a wandering elf ranger with a lifetime of bad memories and a hidden agenda. When the goal of the quest comes within reach, things change irreversibly. That plot might sound fairly generic, but two things make it stand out. One is the excellent worldbuilding--it manages to make elves seem like genuinely different and inhuman beings, and there are some interesting takes on the magic of the setting. The other is the excellent writing, which moves seamlessly between high drama and lowbrow humour, with some shocking or poignant character moments. The pace at which the main plot unfolds is quite slow, with quite a few digressions, side-stories and flashbacks but the trip is entertaining.