Some great recommendations. Let me add a few that I don't think I've seen mentioned (apologies if any of them are redundant):
Alias (no relation to the TV series). Brian Bendis and Michael Gaydos’ masterwork—superhero “deconstruction” told with as much heart as Astro City and as much wit as Hellblazer. Jessica Jones, one-time supeheroine trying to make it as a detective, is one of the few great female characters that either of the Big 2 comic companies have ever produced. It ran 28 issues, available in trade and in a beautiful hardcover collection.
On the subject of Mr. “Love Him or Hate Him” Bendis, his series Powers, with artist Michael Avon Oeming, is a groundbreaking attempt to bring the sensibilities of TV police shows like Homicide or The Wire to superhero comics. It occasionally seems to lose its way over the years, but the first few trades (or hardcover collection) are don’t-miss.
Oh, and since Daredevil’s been mentioned, Bendis with (mostly) artist Alex Maleev just wrapped up the best run on the title since Frank Miller’s (available in trade and hardcover), and the character seems to be headed for possibly even greater heights, currently, in the hands of writer Ed Brubaker and artist Michael Lark.
Brubaker’s also doing a very nice job with Captain America these days—people who’ve never cared for the character at all still seem to be enjoying it.
Invincible. Imagine a teen superhero story told without the need to nurture corporate merchandising. A story that can basically take its characters anywhere it wants to go, and pull surprises of a kind rarely seen from the Big 2. Imagine that it's written with wit, attention to detail, and a strong sense of family; and that it's eye-poppigly colorful, with art so elegantly simple and straightforward that anyone who's read a Sunday newspaper strip can parse it immediately. That would be Robert Kirkman and Cory Walker's Invincible. I read it in trades, so I forget exactly what issue number it's up to. Start with trade #1 and you're hooked.
The Goon. Written and drawn by Eric Powell, it’s like every great issue of EC Comics and Kurtzman-era Mad distilled into one hulking helping of bad attitude. Funniest book on the stands, and one of the most beautifully illustrated.
Bone. If you’ve ever enjoyed any kind of fantasy storytelling, you must try Bone. Imagine, say, The Lord of the Rings written by someone with the sharp wit (and gorgeous brushwork) of Walt Kelly (that would be writer-artist Jeff Smith). Though it’s currently being reissued in color format, the original issues are some of the most beautiful black and white artwork you’ll ever see. For a while, you could get the entire series in one thick, insanely-cheap volume, but even if that’s not available any more, many libraries carry the original trade collections.
Runaways. Brian K Vaughan’s reimagining of the teen superhero as real teens, in a recognizably real world. Never skimps on the action or the laughs, and he’s the master of the cliffhanger. First series ran 18 issues, second series just hit issue 18.
Supreme Power. J. Michael Straczynski’s depiction of the emergence of supeheroes in a world completely unprepared for them (a theme also worth exploring in Straczynski’s earlier Rising Stars series). Artist Gary Frank renders it as something approaching a horror comic (and it was published under Marvel’s adults-only MAX line). 18 issues, available in trades. It’s currently being continued in a non-adults-only form as Squadron Supreme; I’d say the jury’s still out on that one.
Planetary. The “secret history” of the 20th century (the oft-delayed book was supposed to be completed several years ago) turns out to be built from elements as diverse as pulp heroes, Hong Kong movies, incredible monsters, and legendary gunfighters... and the occasional superhero. Writer Warren Ellis can be an acquired taste (some people worship his Transmetropolitan, I find it overrated), but paired with the insanely talented artist John Cassaday, every issue of this series is a compelling read. The final issues should be out later this year. I would also mention that the Planetary/Batman crossover story “Night on Earth” was one of the few decent crossover stories ever written.
Ellis is also writing (with artist Ben Templesmith) a series called Fell: a hard-boiled detective story that brushes up against the supernatural. 16 stunning pages per issue, a complete story each time, for only $1.99.
Cassaday is also doing the art for Joss Whedon’s Astonishing X-Men. There’s nothing unusual enough about it to sway X-haters, but it’s an engaging read that embraces the best of the series’ convoluted past with a nice modern feel.
Garth Ennis’ Preacher has been suggested, and I agree. In addition, he’s currently wriitng the best (only?) Punisher series anyone ever needs, and I recommend all its trade collections. His other great series was Hitman, the story of a hard-drinking gunsel who can’t stand those damn spandex boys, which DC has sadly collected only sporadically. Check your quarter bins—it sometimes turns up there.
Oh, and remember the name Dan Slott: He’s a man besotted with love for comics, and writes stories that both tweak and revere Marvel comics history simultaneously, provide great characterization and engaging plots… and he’s one of the funniest guys around. His short-lived Thing series comes out in trade soon, and his ongoing She-Hulk series is in its second “season”, and may be Marvel’s best current title. Sadly, his very best book, the Spider-Man/Human Torch miniseries he did last year, has been collected in a cramped “digest” format. Try to find the original five issues—Ty Templeton’s art demands it. It’s also the best Spider-Man story AND the best FF story I’ve read in many years.
There's more, but it’s getting late…
