There are so many great ones! Here are my favorites:
For the story and characters: Beast Bait by @dglisson hands down. The leads are incredibly compelling, the layout and design is innovative, and the supernatural action/mystery is very clever. I look forward to every update. I'm a sucker for the X-Files and Buffy, so this hits the right nostalgic notes for me ... but it's most certainly and entirely its own thing.
For the comedy and ridiculousness: Astronaut Ninja by ... Astronaut Ninja. Seriously. An Astronaut Ninja and his telepathic giant Scorpion sidekick on Mars take on little green men and the lead's evil twin Warlock Ninja brother. And it's action-packed, too! And so, so many bad puns.
For the feels: Ingunn Comics by @ingunn . There's so much honesty, so many thought provoking comics. It's bite-sized, so every update is self-contained, not telling an ongoing story ... but full of an ongoing message of acceptance. You can tell that every release is the product of pure love and raw emotion from the artist. It's refreshing, entirely unique, and beautiful.
For the art, part one: Eternity, by Alecyl. Start it for the art, stay for the brutal plot-twists and carnage. It doesn't update frequently, but I'm hoping that it'll be back with a vengeance soon. I'm not a huge vertical scroll comic fan, but (for me) Eternity does it best.
For the art, part two: Scurry, by macsmith. It's an intense story about tribal clans of rodents trying to survive a harsh world full of wild packs of dogs, bullying cats and other monsters. Oh yeah, and maybe it's Post Apocalyptic, and the humans are all gone? It's a mystery. Most importantly, though, the art is unparalleled. The animals are not humanoid, but have so much expression, the characters are distinct with strong perspectives, and the underlying sense of foreboding only continues to build as the protagonists prepare for what promises to be a very, very grand adventure. I don't think I've seen a new webcomic (less than a year old) become so successful so fast -- and it's not through luck. Macsmith is GOOD.