A friend of mine prefers to call them "funny books," and we don't call them comic books anymore, mostly because comic books makes people think of books printed on poor quality paper that rips too easily and tends to bleed ink. I like some graphic novels and I'm going list them here.
Spiegelman's memoirs; Maux, Maux 2, Breakdowns, and In the Shadow of No Towers are wonderful. Breakdowns shows Spiegelman's talents as an artist and show how he uses art to further his narrative. Maus and Maus 2 are great books to introduce people to graphic novels who might shy away from the format. Breakdowns and In the Shadow of No Towers are really for people who enjoy graphic novels, because they both use the art to move the story more than (I think) the earlier two books do.
Marjane Satrapi's memoirs also are a wonderful example of how art should be used to tell stories. The art allows the reader to look at the horrors of life before the revolution but still maintain some distance.
Alice in Sunderland by Bryan Talbot is what happens when someone decides to write a literary biography in a graphic novel format. It is a brilliant idea, because it allows the reader to access the literature on different levels. It's got a full bibliography in the back for people who NEED the references, but there's no reason that literary criticism can't be fun, and this was a brilliant way to address Lewis Carroll's work.
Talbot also wrote "Tale of One Bad Rat," which is both about Beatrix Potter and her short story of the same name, but also how abused children can use both art and literature to help them cope with awful things that happen to them. The heroine of this book is an incest survivor who has run away to escape her abuser. Like Satrapi's books, Talbot uses art to make us look at awful crimes and see them for what they are.