[I wrote this in response to a friend who is just getting into graphic novels and wanted to some orientation.]
These are absolute must-reads:
A Contract with God - considered the first graphic novel, and very good. In reading this you experience the birth of comics in the 70s as more than a throwaway medium.
Understanding Comics - an incredible book that opened my eyes to what comics is and isn't, highly recommended
Fun Home - memoir by a popular indie serial cartoonist about growing up gay, with a very closeted gay dad who missed many chances to connect to his daughter about who they really were. So good that Time magazine named it their book of the year - not graphic novel of the year. What it does with the juxtaposition of image and text is the best argument I know for comics as a medium capable of a distinct kind of greatness from those of prose and illustration.
Watchmen - one of the canonical examples of the superhero revisionism of the 1980s, and a story very well told. (Batman: the Dark Knight Returns is the other big one, and it's interesting for clarifying Batman as a politically conservative hero, but it gets too weird for me to recommend it.)
Ghost World - a great example of the indie comics movement of the 90s, which has a more fluid, varying style that mixes elements of naturalism and surrealism.
Maus - really deserves its lonely place in the small canon of graphic novels respected outside the comics world. You can just read the first volume and you'll get what he is doing artistically. You can see it has some roots in Will Eisner's documentary work, but still connects to Spiegelman's experience in underground comics in the 60s and 70s, which explored absurdism and expressionism, though those are very restrained here.
These are very enjoyable, but not as crucial:
The Walking Dead, volume 1 - addictive, better than the show, quick read
Bone: out from Boneville, by Jeff Smith - silly and delightful
Safe Area Gorazde - comics as contemporary documentary and polemic. Long and intense.
Scott Pilgrim vs the World - wonderful example of the influences of Japanese manga comics and the self-published zine comics of the 90s on current American indie comics. You can start with vol. 1 and see if you like it. Very very fun.
Top Ten volume 1 - my favorite superhero book of the last 15 years, from the insane and genius mind of Alan Moore, who also wrote Watchmen
Persepolis - memoir that uses comics as a medium in genius ways, owes a lot to Spiegelman. Quick read, i think book 1 is better than book 2 so maybe skip that.
Calvin and Hobbes collections - everyone knows this, it's not a graphic novel, but it's soooo good and worth rereading now that we're older
Weapon X - the origin of Wolverine, told in almost incomprehensible fashion so that it reflects the multiple layers of brainwashing and abuse Wolverine went through when he was engineered. Visually breathtaking and meditative. By one of my all time favorite comics artists and writers, Barry Winsor-Smith. Also see his gorgeous exploration of the X-Men character Storm and her godlike powers, Adastra in Africa.