This sort of thread is like my own personal Batsignal.
A few months back, I posted this thread, which was a more-or-less comprehensive list of the webcomics I read at least semi-regularly. For you, I’ll stick to the highlights, based on what you said you were looking for in your OP.
Cat and Girl has got that indie vibe and clever humor of Questionable Content, but with a more literary/intellectual bent. No over-arching storyline, though, more of a gag-a-day thing.
The link isn’t working for me right now, but Digger is a great stroy-based strip about a talking wombat and her difficulties with dieties. It’s on a pay site, but honestly, the three bucks a month is worth it just for this comic. The art is just about the best I’ve ever seen.
Girl Genius is one of my favoritest webcomics ever. It’s a steam punk epic by fan-favorite artist Phil Foglio, and probably the single most frequently linked-to webcomic on the Straight Dope.
Home on the Strange is another QC-like comic. That link goes to the first in the series - the art gets much better later on. Which, come to think of it, is also a lot like QC. It’s themes are more geek-oriented than music-oriented. Lots of jokes about RPGs and Buffy the Vampire Slayer.
Magellan is the best superhero comic out there right now. And by “out there,” I don’t just mean the internet. The story’s been building for three years now, and it looks like it’s finally heading towards a climax, so now’s a great time to jump in.
Something Positive is just about the most fucked up comic out there. That link goes to the first one. If that doesn’t make you instantly love it, run far, far away, because it only gets darker and more misanthropic from there.
Scary Go Round is sort of like Monty Python, except it’s wierd. Very funny, story-based webcomic, with a very distinct ear for dialogue.
Lastly, Narbonic just finished it’s five year run. It’s a three-panel, gag-a-day comic with a great over-arching storyline. The art’s pretty rough at first, but it shapes up nicely by the end of the first year.