Below are comics that I have read which are excellent. Not all of them are about super heros, most are easily accessible so you don't need to know much (or anything at all) before reading.

Blankets is a 600-page black-and-white graphic novel by Craig Thompson, published in 2003 by Shenanigans Productions. A memoir, the book tells the story of Thompson's childhood in an Evangelical Christian family, his first love, and his early adulthood. Thompson has said that the novel grew out of a simple idea: to describe what it feels like to sleep next to someone for the first time.
300 is a historically-inspired 1998 comic book limited series written and illustrated by Frank Miller with painted colors by Lynn Varley. The comic is a retelling of the Battle of Thermopylae and the events leading up to it from the perspective of Leonidas of Sparta.
V for Vendetta is a ten-issue comic book series written by Alan Moore and illustrated mostly by David Lloyd, set in a dystopian future United Kingdom imagined from the 1980s about the 1990s. A mysterious anarchist named "V" works to destroy the totalitarian government, profoundly affecting the people he encounters.
Y: The Last Man is a comic book series by Brian K. Vaughan and Pia Guerra, about the only man to survive the mysterious simultaneous death of every male mammal on Earth. The series has received considerable acclaim from a wide array of critics. The series was published in sixty issues by Vertigo, and collected in a series of 10 paperback volumes.
Watchmen is written by Alan Moore and illustrated by Dave Gibbons. Watchmen is set in 1985, in an alternative history United States where costumed adventurers are real and the country is edging closer to a nuclear war with the Soviet Union (the Doomsday Clock is at five minutes to midnight). It tells the story of a group of past and present superheroes and the events surrounding the mysterious murder of one of their own. To date, Watchmen remains the only graphic novel to win a Hugo Award, and is also the only graphic novel to appear on Time Magazine's 2005 list of "the 100 best English-language novels from 1923 to the present."
Batman: The Long Halloween was a limited series written by Jeph Loeb with art by Tim Sale. It was originally published by DC Comics. The Long Halloween was heavily influenced by film noir and films such as The Godfather. In continuity terms, the series continues and concludes the story of Carmine Falcone who was introduced in Batman: Year One. It also revolves around the gradual transition of Batman's rogues' gallery from simple mob goons to full-fledged supervillains.
Spider-Man: Reign written and illustrated by Kaare Andrews, is set 35 years into Spider-Man's future, it features a retired Spider-Man who returns to combat the injustices of a vastly different New York City.
Kingdom Come written by Mark Waid and painted in gouache by Alex Ross, is set some 20 years into the future of the then-current DC Universe, it deals with a growing conflict between "traditional" superheroes, such as Superman, Wonder Woman, and the Justice League, and a growing population of largely amoral and dangerously irresponsible new vigilantes. Between these two groups is Batman and his assembled team, who attempt to contain the escalating disaster, foil the machinations of Lex Luthor, and prevent a world-ending superhuman war.
Marvels written by Kurt Busiek, painted by Alex Ross, examines the Marvel Universe, the collective setting of most of Marvel's superhero series, from the perspective of an Everyman, news photographer Phil Sheldon. The street-level series portrayed ordinary life in a world full of costumed supermen, with each issue featuring events well-known to readers of Marvel comics as well as a variety of minute details and retelling the most infamous events in the Marvel Universe.
Batman: Hushwritten by Jeph Loeb, and penciled by Jim Lee, depicts a mysterious, eponymous stalker, head wrapped in bandages, that seems intent on sabotaging Batman from afar, and utilizes a large number of guest appearances by Batman villains. It also emphasizes the romantic feelings between Batman and Catwoman.
The Ultimates written by Mark Millar and illustrated by Bryan Hitch, are a superhero team that is a modernized re-imagining of Marvel's long-running super hero team, the Avengers. While the Ultimates are clearly recognizable as a version of the Avengers, they are also very different from the originals. The tone of the stories in these books is widely considered to be darker, more cynical, and more cinematic than most traditional comic books.
Superman: Red Son was written by Mark Millar. In Red Son, Superman's rocket ship lands on a Ukrainian collective farm rather than in Kansas, an implied reason being a small time difference (a handful of hours) from the original timeline, meaning Earth's rotation placed the Ukraine in the ship's path instead of Kansas. Superman is described in Soviet radio broadcasts "... as the Champion of the common worker who fights a never-ending battle for Stalin, socialism, and the international expansion of the Warsaw Pact." It received critical acclaim and was nominated for the 2004 Eisner Award for best limited series.
All Star Superman is written by Grant Morrison, drawn by Frank Quitely. A limited series about Superman slowly dying and what he does with what little time he has. It takes all the silly aspects of Superman and actually makes them good.
Silver Surfer: Requiem by writer J. Michael Straczynski and artist Esad Ribic. For untold years Norrin Radd has surfed the galaxy, exploring the darkness between stars, witnessing the rise and fall of vast civilizations. Now his ride is about to come to an end. It starts with a small spot – a blemish that will spread until he is no more. Until then, the Silver Surfer would undertake his final voyage – to the one destination that has always eluded him. His journey starts where it began.
Ultimate Spider-Man is a superhero comic book series written by Brian Michael Bendis and published by Marvel Comics. The series is a modernized re-imagining of Marvel's long-running Spider-Man comic book franchise as part of its Ultimate Marvel imprint.
Scott Pilgrim is a comedy/action/romance comic series by Bryan Lee O'Malley, intended to eventually consist of six digest-sized black-and-white graphic novels. 23-year-old Canadian Scott Pilgrim, a slacker, hero, wannabe-rockstar, who is living in Toronto and playing bass in the band "Sex Bob-Omb." He falls in love with American delivery girl Ramona V. Flowers, but must defeat her seven "evil exes" in order to date her.