Well, allow me to chip in with some suggestions...
Order of the Stick has been already mentioned, I believe, the art is very minimalist, which can be a turnoff for a new reader, but the artist is great at playing upon and against just about any fantasy trope you can think of and the storyline is nothing if not engaging.
Sluggy Freelance has also been mentioned in the comments. Again, fairly simple art with interesting (if at times ridiculously convoluted and self-referential) writing.
Gunnerkrigg Court is one of my personal favourites, the art is very good and effectively conveys the slightly eerie sci-fi/fairytale feel of the whole series, the story is well thought out and it makes me feel ALL THE FEELS!
I recall Drowtales being cool... Dunno, stopped following it a good while ago, it started getting boring, but the art is very, very good for such a longstanding comic and the whole story is quite unusual and worth checking out.
Homestuck is... interesting. Does it even count as a webcomic? I'd say it kind of skirts the line.
Menage a 3 and its spinoffs are also pretty alright, if frequently NSFW. A slice of life comic with a solid helping of titillation, pretty much.
Least I Could Do used to follow a similar formula, but I feel it grew excessively politicized for my taste somewhere along the line :/
Sandra and Woo also seems popular (and it seems to have been so for a good long while). Again, not a comic I follow myself, but I guess there's got to be something to it?
Schlock Mercenary is nothing if not a classic, it tends to be a pretty easy, action packed read while at the same time running heavy on ideas typical to hard sci-fi. One of the few comics fun both for a quick read and to mull over later.
Freefall is likewise a nice, light take on hard sci-fi, but with far, far less violence and a more slice of life vibe. It also has a much tighter focus, dealing mostly with the idea of a post-scarcity society, terraforming, and especially the implications of conveying "human" rights on artificial intelligence.
Now, there's also Erfworld, a story of a tabletop gamer being summoned into a tabletop game-like world... Not sure if it's quite old enough to qualify as a classic, but it's there and it's pretty good, especially if you dig tabletop strategy gaming.
Of course if I'm not restricting myself exclusively to older titles, there's also stuff like The Punchline is Machismo, Supernormal Step, Paranatural, Skullkickers, Powernap, Spinnerette, Monsterkind, Hark! A Vagrant, Kiwi Blitz (on hiatus until spring, but you can check out the author's other work too), maaaybe Grrl Power and Guilded Age... Daughter of the Lilies, Wilde Life (both mentioned here earlier) and Cassiopeia Quinn are all interesting too, but it looks like they're just getting started on the action now that all the characters have been introduced.
P.S. I take it we're only talking about comics, that originated on the 'net? Because stuff like Peanuts is also published online nowadays, technically making it a webcomic and while I may not personally enjoy it, it's ingrained in the popular culture moreso than any other title mentioned so far in the article or in this thread.
