I contend that comics are a medium and not a style. When most people hear "comics", they imagine the oft-ridiculous superhero-type of story and artwork. There's a lot more to that, of course, and I like a lot of those other things. However, I like the superhero stuff, and I feel that the serial, eternal nature of superhero comics has a special place in the world of pop culture. Craig Thompson's Blankets is great stuff, but it's not the same as years and years and years of comics about the same character. In addition, the over-the-top style of superhero, sci-fi, fantasy comics provides a lot of narrative ammo that doesn't, and can't, exist in other mediums and styles. Think about science fiction TV shows and movies using off-the-wall scenarios to describe the author's feelings about current events or culture.
What I'm getting at is that while it's easy for comic aficionados to recommend something like Blankets or Pride of Baghdad because it doesn't have any of the "weird" shit that exists in superhero comics, but superhero comics have value too, and I do think that general audiences should at least give it a try.
However, most superhero comics are operating on decades, literally decades, of characterization and development. We're to the point in our culture where we all know quite a bit about Wolverine or Batman; We can describe their characters in detail, their character histories and their relationships to other characters. But if a non-comic reader picked up your average Marvel or DC comic, they wouldn't know what the fuck was going on. "Oh, Frenzy has a problem with Pietro because of that thing that happened in the Apocalypse alternative universe, I understand perfectly!" Actually, I read a ton of comics and I'm not even sure what I just wrote is correct.
Right now, the best comics that I've ever read and are reading are Uncanny Avengers, Uncanny X-Force and Superior Spider-Man. These are by far the best things to read right now, but I can't recommend them easily because it requires knowing a lot of the history of the characters, as well as being accepting of the weird superhero shit that shows up here.
With that in mind, I wanted to give special mention to a few comics that I think are good for warming people up to the superhero-style or comics that don't need much back story knowledge to appreciate.
Saga - Brian K. Vaughan wrote Y: The Last Man and Pride of Baghdad, which are some of the best comics ever written. Saga is 18 issues in and is...impossible to explain. It's something like Romeo and Juliet meets Star Wars, I guess? It's the story of a couple trying to raise their child, but there are...robots and...cats? It's hard to explain but the characterization and artwork is superb.
Sex Criminals - This one is written by Matt Fraction and it tells the story of a young woman who stops time when she orgasms. Not making that up. Fraction's writing is fast-paced and casual, while still taking the time to be charming and quaint. This is only 3 or so issues in.
Hawkeye - If I had to recommend one comic as an introduction to comics or an introduction to superhero comics, it would be this one. This one is also written by Fraction, and focuses mainly on the day-to-day life of a superhero when he's not superheroing. The 16th issue just came out.
Black Science and Deadly Class - Both of these are written by Rick Remender, whom I've written about before. Black Science is extremely and intentionally campy. Deadly Class is only 1 issue in, which makes it hard to recommend, but I know Remender is a great writer, so I have high hopes for it.
Black Widow - This one is written by someone whom I haven't heard of before, but the art is by Phil Noto, whose work is amazing.
The story is progressing slowly, not a lot of characters, not an overarching plot yet, but I'm enjoying the long play, and I have hopes for this one.