Lackadaisy - seriously, why have you not read this yet?
Girls With Slingshots - quirky comedy stuff about lesbians. Said lesbians lack slingshots. Disappointed, but otherwise a great comic
Homestuck - it's tedious and at times not very funny, but it's worth reading simply because of its legacy and hilariously complex story that just kind of gives up on making sense halfway through. It's hard to describe in just one sentence, so let me just call it a "thing". It's a thing with GIFs. It's a thing with hours of flash animation. It's a thing with a movie-length soundtrack. It's a thing with about 4 protagonists to 16 central characters (though still focusing on the 4 main characters most of time) in about an arc and a half. It's a thing, a thing that is basically one ridiculously long, complex, and batshit insane love letter to Earthbound.
Zoophobia - gorgeously illustrated and charming in its simplicity, it's not particularly dramatic and its main focus is comedy, with a dash of nightmarish horror time and time again
Cucumber Quest - by that woman who did Hiimdaisy (that's Hi, I'm Daisy). It's charming, silly and funny, and the art's a nice blend of retro and video-game inspired scribbling
Gunnerkrig Court - a fantasy, genre-blending thing. While the art starts of as simplistic and a little jarring, it improves rapidly, to a professional level. I reccomend that everybody reads this wonderful comic.
Ozzie and Millie - it's a comic about children. That's, like, it. Just about children. Doing children things. No time travel, universal retcons, coming out stories or the abritrarily complex plots. It's just... about children being adorable. That's it, really.
The Fox Sister - it's a fairly new comic by an artist I love.
Kiskaloo - by the guy who directed the story and art for Lilo and Stitch. That enough should tell you whether you'll like it.
Minus - a rather prolific comic about a reality-warping little girl. It talks about subjects such as art, science, religion and pretty much anything cultural.
Cat and Girl - a long-running comic about an optimist and a Nietzche wannabe. It uses the style of a comic strip, having no real overarching story. Still a very good comic.
The Meek - a fantasy comic by a biology teacher. It's beautiful and complicated, so you'll need to pay attention if you want to understand it. Seriously, nothing makes sense if you just mull over it, and it's entirely intentional.
Hark, A Vagrant! - it's a comic about history, literature and feminists. Occasionally includes artsy nipples and has provided many a meme. The author is also a legit historian and artist, so you might learn a thing amidst the hilarious satire.
A few NSFW ones include DAR! and the other works of Erika Moen (all of which are horrendously NSFW. Not pornographic as much as they are erotic, including things like sex information and covering pretty much everything to do with the sex industry), and Oglaf (again, insanely NSFW. It's a sex comedy full of fanservice of any kind you could name, and it doesn't have any shame).