Personal Thoughts:
The only webcomics I seriously read (through the archives of, check every day, etc.) are usually at least three-a-week comedy-with-some-drama strips with large casts and some characters I reasonably care about. You know, like this one, or Something Positive. Penny & Aggie is another favorite. Generally, if I go on Wikipedia and find entries for about twenty people (but not fifty, like SOME fantasy strips I know of...), five of whom are pretty important, that's a pretty good sign. It needs to be either funny joke-wise, or funny observation-wise, and each comic gets at least one or two 'sad' things (S*P's got Faye dying and Davan generally being depressed about friends going away; QC has Faye's dad, P&A have Penny's mom) to be important, without going overboard on the drama (Queen of Wands comes to mind).
Good art is a positive, but not a must. I forgive Randy Milholland's static 'everyone is built the same' style because he's at least consistent and does what is needed, and his strip is actually hilarious and all.
I read a few 'gag a day' type strips, but not seriously, and I usually only check up on them every once in a while (Dinosaur Comics, Perry Bible Fellowship, etc.). Gamer comics are iffy, because I'm not a gamer and am likely to miss any topical humor in them (I love VG Cats, but HOLY CRAP do some strips just go way over my head). I used to be really into Penny Arcade, but fell out of it once I got NONE of the jokes.
I HATE HATE HATE fantasy strips. I don't know WHY, but I do. They're all too similar: It's either a gag strip of "hahah! he's riding a funny mount!" and "let's poke fun at a fantasy archetype, like dumb orcs or easy to kill low-level threats!" type jokes, or a super-jokey strip that's impossible to take seriously because they stick in too many epic plotlines (or vice versa).
I also don't read "manga drawn by white people" strips. Every one I've read just screams of my fellow honkies trying desperately to be an 'egg' (you know, white on the outside, yellow on the inside) and all Japanese, and it usually ends up being WAY too emo and instead of having any semblance of what Japanese comics are actually like, try to pull off EVERY MANGA STEREOTYPE in the span of five pages. Even the more sane ones, like Red String, tend to devolve into "WAAAAAAAHHHH EVERY CHARACTER IS A PIT OF EXAGGERATED EMOTIONS!" situations.