If you want a taste of the classics, and as I do, absolutely hate superhero bullshit, well then you must read The Complete Maus. I've never been into comic books or superheroes, but I remember being blown away when I discovered Maus. http://www.goodreads.com/book/show/15195.The_Complete_Maus
Saga. @khrm was asking about it, so I'll post my response here for your edification:
Brian K. Vaughan's seminal meisterwork (IMO). They're graphic novels/comics, informed as much by Star Wars as Liquid TV and other semi-obscure animation geared toward a more adult demographic. It's about a young family; Mum and Dad are from opposing sides of an interstellar proxy war, yet fall in love and are on the run with their newborn from both sides because of the danger their romance presents to established cultural narratives and agitprop, as well as myriad bizarre characters, bounty hunters, secessionists, philosophers, disembowelled ghost teenagers, etc.
It's great fun, offers some thoughtful views on armed conflict and politics, but it's very character and relationship driven with some charming and all-too-familiar renditions of what constitutes parenthood. A thoroughly engaging and entertaining world that parallels much of our own, though definitely not for younger readers. A heart-warming, provocative, and endearing adventure thus far, so I'm looking forward to getting the next volume. Recommend it, lighter in some ways though there's still all the moral ambiguity of the real world present and accounted for - but there's a balancing element of hope and perseverance which charmed the hell out of me. A sort of you-and-me against the universe, with Arachnid bounty-hunter wet dreams, talking cats, Robot monarchies, and an organic tree-rocketship. It's that good
Don't start with Sandman. The reason I say this is once you do, nothing else will really compare. In my humble opinion, everything else pales in comparison to Sandman. It's probably my favorite series ever, graphic or otherwise.
I have to third the recommendation for Maus. It's essential and it's fantastic. Are there any genres within Graphic Novels you're thinking of specifically because I could recommend a very wide range of things. The Walking Dead is amazing (and in my opinion is better than the show). Seconds and Lost at Sea by Bryan O'Malley (also did Scott Pilgrim). Ghost World, Saga, V for Vendetta, Persepolis, Watchmen, and Fun Home are some of my other recommendations.
OMG, that's a magazine I haven't read a reference to in ages... Omni!
My dad had a subscription to Omni. After he was done with it every month, it belonged to me!
What great covers, a mix of hard science and speculative science, interviews, fiction... with all the crap out there, it's not fair that Omni went under.
I just finished 3 compendiums of the the Walking Dead series. 1000+ pages each. They combine about 40 comics in 1 big book, which makes it resemble a graphic novel. The comics are awesome, way way better than the tv-show. I can definitely recommend it. Oh, one last thing; the art in the panels is all in black and white. Some people might not like this, but in my opinion it adds to the tone.