My favorite right now is Kagerou. So as not to give too much of the plot away, I'll just say that it's about a boy- Kago- with MPD and a troubled past. He gets selected as a Champion by a princess in another land who wants him to fight a human who has found out the power of the gods, on behalf of a goddess who's trying to bond with the princess. Only, as the story progresses, he finds out that the goddess might not be the best one to follow, and that's only one of his - and the princess's, and the whole cast's - problems... (I know, I know, it sounds really cliche, but the art is stunning (and in color!) and the story line - and Kano's past - is more convulted than it might originally seem. It takes a while to pick up, but if you stick with it, you should be rewarded!) The comic currently stands at 33 chapters completed, and updates pretty regularly. There's also an lj community - kageroumanga.
Another good one is Fallen. It's about a Guardian (think angel, only different) who is banished to Earth and the girl who takes pity on him and lets him (and his dragon-girl watcher) move in. It's set in a sort-of alternate Earth, and has a interesting background/backplot and a plot with quite a few twists and turns along the way. Brilliant art - the artists captures expressions well, I think. There are two parts currently completed (each with 5-6 chapters), and the third part is mostly completed.
Moving on to some gender-swapping (ah, now I've got your attention!), Misfile is a good one. It's about an alcoholic, druggie angel who accidently misfiles two teen's files, so that one becomes a girl and the other loses two years of her life (instead of a senior, she's now back to being a sophmore, etc). The angel gets kicked out of heaven for smoking cannabis on the job, but the misfile gets overlooked, which is good news for the teens involved, because if it had, they would be fixed like that - forever. The angel, Rumisiel, moves in with Ash (the guy-to-girl) so that Ash can keep an eye on him until he does enough good deeds to get back into heaven, where he can fix his clerical error, and as you may well guess, antics ensue - especially when Rumisiel's brother, who doesn't know about the mix-up, moves in as well and develops a crush on Ash. There are four books currently completed.
Another comic that I rather enjoy is Krakow. It's about two roomates in college - one has a history of rather abusive girlfriends and the other has a succubus as a girlfriend (or rather, has had a succubus as a girlfriend for most of the comic.) It's rather cute, even though the art is rather (read: extremely) simplistic.
Another one by this artist is Marilith, about an assassin and her apprentice who's just trying to get enough jobs- and enough money- to retire. Of course, nothing's ever that easy... The art and storyline are extremely different than that of Krakow's, if more mature and dark.
And one last one: Venus Envy! This one's about a Male-To-Female and her struggle to fit in and keep her real technical gender a secret - rather hard, considering she's always going on dates and is a star of the girl's soccer team! It's also about her struggles with her family - her mom wants Alex back, her dad supports her but is almost always overruled by her mom, and her brother harbors some serious resentment for making them move from their last town/high school, where they were getting physical threats. Add in a disproportionate number of lesbians, a paranoid Female-To-Male, a punk-goth psychic, and who knows what else, and you've got yourselves a hell of a comic! The art isn't exactly what you'd call top of the line, but with a story line like that, who cares?
I'm always on the lookout for new web-comics, so if you see some you'd think I'd like... *hint, hint*