Want a foolproof way to get some good graphic novels to read? Grab any edition of The Year's Best Fantasy and Horror - the ones edited by Terri Windling and Ellen Datlow (at least until a couple of years ago, when Windling stepped down and was succeeded by Kelly Link and Gavin J. Grant), look in the introductory essays for the one on the year's best graphic novels, and make a reading list from that essay's recommendations. You won't go wrong, and you'll find a lot of amazing stuff across all genres. (And now you'll have plenty of time to catch up, as the YBFH series has apparently been discontinued, damn it all.)
A case in point is Bookhunter, by Jason Shiga. A rare book is stolen from the Oakland Public Library, and the Library Police are dispatched to investigate the theft. Who are the Library Police? They're a crack squad of law enforcement professionals who are charged with protecting American access to information via the libraries, and they investigate the theft of the rare book with meticulous attention to detail and good old fashioned gumshoeing.
The story is set in the 1970s, so the overall tone is kind of like CSI meets Kojak. The book is full of fun information about books, and about libraries and library procedures; and of course, the entire conceit is hilarious, right down to the last fight where the villain is able to jump-start his final getaway attempt by using the drawers of the card catalog to his advantage. This is a wildly fun and entertaining book.
Not wildly fun is Shaun Tan's The Arrival; this book is stunningly beautiful instead, a true work of art that puts the very best of comics on display for anyone who may still be skeptical as to whether comics are a viable medium for deep storytelling. This tale of immigration is told through illustrations only; there isn't a single word anywhere in the book. But what illustrations they are: evocative, haunting, and all of them beautiful. This book reminds me of the work of David Wiesner in its sophisticated use of nothing but image to tell an involving story. A man comes to a new country, where he's immediately baffled by the customs he finds and the sprawling cityscape in which he must live. But he manages, through the help of new friends, some of whom aren't human or any recognizable species at all. The way this book uses the fantastic to make statements about the universal experience of people who voyage to a new homeland is nothing short of amazing. This is a gorgeously wonderful book.
I also note the anthology series Flight, whose fifth installment came out last year. For some reason I'd had the impression that the Flight books present excerpts from long-form works, but that's incorrect; the pieces in each volume of Flight are complete, and the books are basically collections of short fiction, just in the comics medium. I'm not going to cite specific examples of effective stories here, but each volume thus far contains some absolute gems. Give Flight a look.