OGLAF

Kill Six Billion Demons is my favorite right now. Gorgeous, sprawling, complex artwork from start to finish, philosophically interesting, bordering on pretentious but I love it. I sometimes read this one while wearing my VR headset to properly examine certain pages close up.

Johnny Wander is the homepage for an incredible artist/writer duo. I've really been enjoying their latest story Barbarous, but their archives are a bit of a pain to navigate to find the starting point for each story. Worth the pain though.

Octopus Pie has been over for a few years but is always worth returning to. Woman lives in New York, people are weird, and New York has a lot of people. Reading this one will make you feel good, Do Not Skip.

Sleepless Domain is an interesting one, generally a cutesy story with an anime, leaning towards chibi art style but focused around a set of brutal murders that happen towards the front end of the story and the survivor's guilt that follows.

Gunnerkrigg Court is hard for me to describe but gets a re-read from me every few years. A surreal examination of why we tell stories and The Power Of Friendship? It's been going so long that I half suspect it's not going anywhere and is just an excuse to keep chugging for as many years as its author needs it to, and also half suspect it's imminently ending in the next few months. I don't think I really have a problem with it either way; it's written very well.

I also want to add Questionable Content. Someone else mentioned it before but I think it needs linking to. It's one of the first webcomics I picked up so it's hard for me to judge it fairly, but even having evolved so much since the early days I think there's something to love about every stage of its development. It was just easy reading about hipsters listening to music and drinking coffee, and then somewhere along the way it became a sci-fi story too and goodness I love it.

I'm partial to weird fantasy, dunno what your tastes are. YMMV. Some of these are old!

Gunnerkrigg Court - long-running, fantastic worldbuilding, intricate plot. steampunky urban fantasy.

Wilde Life - small-town mystery, light spooky vibes but mostly feel-good. Relationship focused.

Girls with Slingshots - complete! comedy about a friend group. LGBT+ themes, sex positive. A bit raunchy, if that's not your bag.

Skin Deep - urban fantasy. Neat worldbuilding, long running.

Broodhollow - another small-town mystery, but more legit creepy. Plot of the murder-hauntings-cults variety.

Manly Guys Doing Manly Things - comedy. premise is a temp agency for brawny fictional characters & villains trying to get normal dayjobs. Takes the piss out of common tropes.

Awkward Zombie - comedy. No plot, just comics about video games & other things the artist is into.

Johnny Wander - 4 comics in a trenchcoat, but they're all pretty cute. Started as an autobio comic with the occasional original fiction story mixed in, but they've all been separated out for easier reading now.

The Less Than Epic Adventures of TJ and Amal - complete! romance about two dudes on a cross-country roadtrip. Touches on some heavy topics, but has some humor too.

A lot of these are hosted by sites that host other comics, so you can follow that rabbit hole pretty far. Also some artists will link to other comics they like in the about/notes pages, good way to find other stuff.

Xkcd, Saturday morning breakfast cereal, something positive, questionable content, and Junior scientist power hour are my favorites.

How about my comic? Hehe

Seriously though Gone with the Blastwave is something I always come back to once in awhile

@LaunchesKayaks

Kill 6 Billion Demons is an absolute classic. Good enought to have made it into print trade paperbacks, but still free online. The visual style and wild world building are truly a joy to behold. You also get a bit of the sparky web comic flavor while still holding together an excellent long term story arc with serious plot.

https://killsixbilliondemons.com/comic/kill-six-billion-demons-chapter-1/

Girl Genius is one of my favorite. https://www.girlgeniusonline.com/comic.php

Free Fall was a very good sf web comic whose first story arc is completed, so jump right in. Several interesting non-human characters.

http://freefall.purrsia.com/ff100/fv00001.htm

I'm showing my age here, but 8-bit theater is fun

https://www.nuklearpower.com/2001/03/02/episode-001-were-going-where/

Personally a big fan of hiveworks for finding new comics. If you like story focused ones, I like Widdershins, Sakana, Daughter of the Lilies, and Wilde Life. I read way too many webcomics, so let me know if you need more!

Can I sell you on web novels instead? Worm and The Wandering Inn are a decent starting point.

Blast the Wave https://www.blastwave-comic.com/index.php?p=comic&nro=1

Have you read Vattu? It's hands down one of my favorite comics ever.

Stand Still, Stay Silent is also pretty good.

Bato.to

My favorite are Dr. Frost and Solo Leveling

Digger by Ursula Vernon has been around for a while but it's my favourite.

Penny Arcade has been around forever so they have a deep backlog of gaming/nerd culture related comics.

Schlock Mercenary (complete)
Goblins
Freakangels
Grrl power
Order of the stick

If you need a comic that won't run out, you can try EGS. A comic about teens running into a wide variety of supernatural stuff.
https://www.egscomics.com/
It's been running since 2002 and still going. And while the early arc are pretty rough in both art style and writing quality, it gets progressively better as the author matures.

Another comic I love is Sleepless Domain, a dark magical girl story about a locked down city that comes under monster attack every night.
https://www.sleeplessdomain.com/

I found both of these through https://hiveworkscomics.com/ which is another, though smaller comic repository like Webtoons.

https://mrlovenstein.com/

Irregular Webcomic: it's mostly reruns these days with new strips twice a week. Still, there is a lot of material to get caught up on.

I enjoy Adventures of God if you want another webtoons comic

I Roved Out. Extremely NSFW, it would be categorized as porn. It is an incredible story, and is so despite the porn. The sex is so interwoven with the story, I can't imagine a SFW version could ever be constructed, which is shame because it's such good art, and such a great story. I can't praise it enough. If graphic sex doesn't bother you, I highly recommend it.

Blastwave. Short, so if you binge it it'll be over quickly.

There have been other great recommendations I won't repeat, but these two have exceptional art.

Edit someone else beat me to recommending Blastwave. It's good.

Something Positive is great and fun to start from the beginning.

Queen of Wands ended a while ago but was entertaining.

Dumbing of Age is fun, but the creator has also made several other comics based on a lot of similar characters. You can check them out too.

@LaunchesKayaks my favs:

https://www.grrlpowercomic.com/
https://questionablecontent.net/index.php
http://www.threepanelsoul.com/

Long histories, interesting characters/world building, cool art.

To go a different style, 8bit theater and adventurers are a blast if you like the RPG parody style

Loving Reaper by Jenny Jinya.

Astral Aves sort of stopped updating a while back, but what there is of it is absolutely amazing.

I like Texts From Superheroes.

Narbonic and its successor Skin Horse are both now complete and never get the love I feel they deserve.

Shag & Scoob

East Coast Its isn't any kind of serialized or contiguous, but it is free and great. On the opposite end of the spectrum, here's a free unofficial translation of One Punch Man, which is highly serialized and contiguous.

What are your preferences? Currently I'm reading this

https://bato.to/series/133684/the-killing-vote

https://bato.to/series/103401/a-bona-fide-killer

https://bato.to/series/118271/granny-official

https://www.webtoons.com/en/romance/my-reason-to-die/list?title_no=3993