Classic webcomic that spawned a lot of frequently reposted images and quotes that you've likely seen before.
Manga
Nausicaa of the Valley of the Wind
by Hayao Miyazaki
After the end of the world, a princess who loves insects and hates killing tries to keep peace in a quickly escalating conflict.
Dungeon Meshi
by Ryoko Kui
Laius and his party return to a dungeon to save his sister after she was eaten by a dragon - and, as they can't afford food, decide to eat the monsters.
Dorohedoro
by Q Hayashida
Gruesome and creative. Dorohedoro is a story about food and friendship, and a terrible, grotesque mystery.
Full Metal Alchemist
by Hiromu Arakawa
Alchemist brothers, Ed and Alphonse Elric, journey to search for a way to restore their bodies after making a terrible mistake.
Mob Psycho 100
by ONE
A powerful esper named Mob learns to deal with his incredible psychic powers, as well as his tendency to bottle up his own emotions to control them.
My Lesbian Experience with Loneliness
by Nagata Kabi
An autobiographical comic diary of an artist's struggle with loneliness and intimacy.
The Way of the Househusband
by Kousuke Oono
Follow an ex-yakuza boss who retires from crime to become a househusband.