I never even knew the other thread existed.
Where the hell was I when that happened?
Anyhow, there are far too many web-comics that I enjoy reading so I'll avoid putting down ones that have already been said, and I'll post just five.
JACK -- I can't link to it due to its content, but I'll go ahead and quote an excellent description of it:
"An amazing strip of grotesque beauty. Life, death, horror, love ... this is a masterful use of the sequential art medium. And don't be fooled by the fuzzy characters, this strip is 100% FOR ADULTS ONLY! NC-17 for sure. "
The Parking Lot is Full (PLIF) -- PLIF is probably one of the oldest web-comics in existance. It has been retired now, but it's still full of cynical charm and sardonic wit. I also can not link to this one due to its content. (This is where that comic about eating your clones comes from.) In fact, I think most would find PLIF more offensive than JACK. :p
Scary-Go-Round is an awesome comic that details the odd happenings of the main cast, (an odd, friendly girl, two slackers, a female super-agent, and a genius inventor.) The comic is broken down into chapters and each chapter tends to focus mainly on one or two of the characters. The best way I could classify the genre of this comic would be a comedy-drama that's semi-grounded in reality with a slight dash of dark humor.
Powerpuff Girls Doujinshi -- While "doujinshi" is often associated with hentai, it really just means "fan-comic." Bleedman (the artist of the comic,) and his friends have a real knack for taking existing characters (just about every recent cartoon that has aired on Cartoon Network,) and masterfully weaving them together into an awesome and somewhat emotional story. Bleedman does tend to update sporadically, but every comic is lush with detail and color.
Radioactive Panda -- I really had a hard time choosing the fifth one, but I decided to go with a lesser-known, humorous comic. Radioactive Panda is essentially about the lives of two mad scientists and their werewolf friend. After being forced out of their castle by a mob of angry villagers, they take residence underneath a Chinese restaraunt where a former mad scientist dwelled. There they hang out with some of the employees of the restaurant, three zombie guys, and several other creatures that lurk about.
And there you go... that's about a 1/5 or so of the web-comics I read. I hope I didn't sound too artsy in describing them. I hate being artsy, but I don't think "I like this comic, because it's cool." is very helpful.