For manga:
Ghost in the Shell and Appleseed by Masamune Shirow are very influential and well known (in the west) scifi manga, but they are pretty dense and technical and not everyone's cup of tea. Both go into a lot of very detailed world building and politics, but also have some of the coolest Japanese cyberpunk action every put to page.
Berserk by Kentaro Miura is probably the most famous fantasy manga in the west. Unrelentingly dark and grim, it isn't to everyone's taste but the spectacular art and unique, epic story make it stand out in the genre. Contains some nasty sexual violence.
Fullmetal Alchemist is a steampunk fantasy setting with great characters and story. It's aimed at a younger audience but mostly avoids the common tropes and cliches of that style. Easy to read and charismatic series.
For graphic novels:
I can't avoid bringing up Alan Moore's Watchmen. Probably the most influential graphic novel ever written, it is a masterpiece on every level. Even if you're not into superhero comics (which this is kind of a deconstruction of) the story stands on its own.
The Sandman series by Neil Gaiman. Feel free to pirate these considering Gaiman has turned out to be a piece of human garbage. But you can't deny the mastery of this series. Gothic, romantic fantasy with incredible depth, beauty and power.
Saga by Brian K. Vaughan is a popular space opera series by one of the best writers in comics. Just really charismatic and engaging, great art, great characters and a narrative that effortlessly carries you along for the ride.
Sweet Tooth by Jeff Lemire is a strange, unique post apocalypse story. Great writing and characters but very dark and the overarching plot is kind of weird (but not really the point of the story).
Preacher by Garth Ennis is a modern fantasy with some of the sharpest writing in comics and a brilliant concept. I'd compare it to a Tarantino film where the overarching story is just an excuse for razor sharp dialogue and ultra-stylish characters and scenes (but the overarching story is great, too). Be warned that Ennis loves over the top shock and gross outs, which I personally find tedious but put up with because the rest is so good. Note that I think the second half of the series (there's a major event and small time skip at this point) is kind of dull and self-indulgent and can essentially be avoided.