Out of the set of those that haven't already been mentioned in this thread, I'd particularly recommend Narbonic/Skin Horse, Iothera, Bad Machinery, JL8, and The Last Halloween to this group.Here is the subset of webcomics I have bookmarked/RSS'd that I think might be of interest to this group of people. Skipping things like SMBC, Homestuck, XKCD, etc. which I'm sure everyone already knows about.
Irregular Webcomic Huge archive (over 3000 strips) of 3-panel format strips Skips between multiple distinct continuities (with occasional crossovers). Focus is on jokes rather than plot, usually. Be sure to read the annotations.
Questionable Content Mostly a relationship comic, though there are some light sci-fi/singularity elements lurking in the background. Focus is on characterization. Has a very slow-moving plot, but strip is nearing 3000 comics so a lot has happened.
Skin Horse Hard to describe, but insanely good. Loose sequel to the completed Narbonic, a webcomic about mad science which is one of my favorite comics of all time.
Scary Go Round Set in the fictional British town of Tackleford, slice-of-life comic with a huge ensemble cast involving frequent fantasy/sci-fi/occult elements. Spans multiple separate comics in the same continuity written consistently since 1998. A good place to start is with Bad Machinery, a recently-concluded sub-webcomic with a tighter set of characters (mystery-solving teens). Then you can go back and pick up the earlier stuff if it appeals.
Dinosaur Comics Very text-focused: the same six panels of art are recycled for every strip. A consistent set of characters, but no real continuity or notion of a fourth wall. Written by Ryan North, who started as a grad student in linguistics and is now a professional web...person...who you've probably heard of. Has alt-text like XKCD, but there are three sources of it (image mouseover, RSS title, contact email subject) every day--I use this Chrome extension to read.
Gunnerkrigg Court Frequently described as "like Harry Potter", but that's not really true at all except that it's set at a hidden boarding school in a world like ours but with magical and mythical elements. Probably my favorite webcomic of the ones I'm currently reading. Wonderful characterization, fascinating plot, outstanding worldbuilding.
Iothera Hard to describe the plot, but it involves space travel in a world where technology is powered by magic rather than electronics. Probably the most detailed art and worldbuilding of any webcomic I've seen. Warnings: this is the third (at least) incarnation of the webcomic. The previous versions were called Midlands and Heliothaumic, and are very hard to find. The webcomic updates glacially slowly. And it is decidedly and explicitly (though tastefully and not gratuitously) NSFW.
Strong Female Protagonist Has been linked here before.
JL8 The Justice League as 8-year-olds. Very cute.
Dumbing of Age Slice-of-life comic at a midwestern college. Focus is on characterization. There are previous comics with different incarnations of these characters in a more sci-fi setting, but try this first.
Darths & Droids Screencap The premise is that the Star Wars movies are a D&D game. Inspired by the immortal DM of the Rings, which did the same thing for LOTR.
The Last Halloween Beautiful weekly horror/humor comic.
Goats Starts off as surreal slice-of-life with fantastical elements, very quickly accelerates to the fantastical/sci-fi elements taking over the strip. The strip started in 1997, but the current archives begin in 2003, right at the beginning of this acceleration. On semi-permanent hiatus.
Transdimensional Brain Chip Terrible art, meh characters, interesting plot. Best binge-read.
It looks like I've added 2 new comics to my RSS reader since I wrote that list: Cucumber Quest, which I second (third?) the recommendation of, and It's a Hard Life, a Pokemon comic (a Nuzlocke comic specifically, if that means anything to you, but not one typical to that genre) whose art is painted watercolors; it starts out a little ugly but becomes progressively more and more beautiful even as the plot becomes more and more heartwrenching. I realize the first few pages are pretty stupid but, if you care at all about Pokemon, I really urge you to give it a little bit of time (at least finish Chapter 1 before you give it up); it's worth it, trust me.