Here are some awesome comics that you should read. Forever.
Girl Genius - The comic that got me into steampunk and an exceedingly long runner with a spotless update record. The art has only improved over its many years, and while the writing can sometimes get a bit too stuck on certain small plot events, overall it is some ridiculously top-notch stuff. Well worth your time.
Penny Arcade - Do I even need to link to this? Is that a thing I should do? Most people who read greater than three webcomics probably know about Penny Arcade. The dialogue nearly always sparkles, the art constantly shows effort and refining, and the blog posts are amusingly written. Blah blah blah praise.
MS Paint Adventures - I got into MSPA when Problem Sleuth was about a third through, and overall still prefer that one slightly to the current adventure, Homestuck, but regardless Andrew Hussie is doing some pretty amazing things with the webcomics medium and you should give it a look-see. This is good natively-digital stuff.
Spinnerette - A wonderfully-done affectionate parody of Spider-Man that I just got into recently, but captured me enough to recommend it here. It has a field day poking fun at various superhero cliches and does it well, while still also telling a perfectly legit superhero story of its own no less.
Wondermark - Victorian engravings x clever dialogue = humor magic.
Dinosaur Comics - One of the best comics featuring static images of dinosaurs, possibly! Since the panels are always the same, Dinosaur Comics must rely on the strength of its writing; it is fortunately strong writing indeed.
Exploding Kitties - Endless variations on a simple premise: "adorable kitten dies horribly."
The Punchline Is Machismo - The laugh-filled and occasionally genuinely heartwarming story of the manliest man to ever man men. Manly.
Guttersnipe - The most humor you can wring out of the Great Depression. Mr. Rosen, the creator, has a very kinetic, John Kricfalusi-esque art style that delivers a high dose of funny on its own, and his smirking writing is where he shines. Also, I totally did the colour work for the cover of a graphic novel he has coming out, so, y'know, that's cool too.
Intragalactic - A fun, albeit currently on very limited update schedule, strip that plays with science-fiction tropes, reimagining a Captain Kirk archetype as the female commander of an interplanetary ice cream truck.
Pictures For Sad Children - Pretty much as soon as you see this comic, you will find it was one of the two main inspirations for CWAP. Except that PFSC is much, much better-written. There is an absolute art in this comic to making morose or awkward situations hilarious, and the minimalist artwork somehow enhances it.
Chainsawsuit - The other big inspiration for CWAP, which you will again see pretty much as soon as you take a look at it. I think Kris Straub could make a comic out of potentially any premise. And frequently does.
Hark! A Vagrant - You're going to notice a trend in these webcomics recommendations. That trend is "good writing." Kate Beaton continues that trend firmly. It may be a history webcomic but maaaaaan, you don't even need to know much history to get a good laugh out of it. And if you do know the history it is DOUBLY humorous.
Perry Bible Fellowship - Glorious sharp quick tragicomedy, and the continual variations in artwork are always fun. Sadly on indefinite hiatus.
Girls With Slingshots - Roommates, a bar, and layers and layers of multifaceted character relationships. And a talking cactus, but I think you'll actually find yourself laughing far more at the humor (and going wide-eyed at the drama) that results entirely via the main casts' reactions to each other.
Shortpacked! - A webcomic about the staff of a large toy store, rich with comics-and-toy humor and thick with character developments. Manages both extremes of "serious moment" and "absolutely ludicrous" quite well, mostly sticks to the silly end of things. Ethan, the main character, also gets points for being possibly one of the least stereotypically-behaving gay male characters in major webcomics that I've come across.
Templar, Arizona - I have a thing for fictional (and true, as well) slice-of-life comics. That is totally my kettle of fish. Things like that are going to keep happening on this list. Spike, the creator of this comic, has put an insane amount of effort into the world-building, and it shows.
Wonderella - If you ever asked yourself, "what would Wonder Woman be like if she were a humorously selfish, irresponsible prick?" here's your chance to find out. Has a very interesting art deco art style that's worth taking a peek at in of itself.
Weapon Brown - Do you like comic strip history? Do you like poking fun at gritty 90s anti-hero comics? Jason Yungbluth has you covered both ways with an epic, sprawling, reference-loaded tale of a grim super-soldier Charlie Brown in a post-apocalyptic wasteland. Seriously.
Concrete, by Paul Chadwick --A speechwriter's life is changed forever when his brain is transplanted into the body of a 9-foot-tall, thousand-pound rock monster.
Koko Be Good, by Jen Wang -- A recent discovery that became a fast personal favourite I'd recommend to nearly anyone. Jen Wang's artwork, in particular, is absolutely gorgeous--everyone's seemingly made out of cartoony rubber but still has a sense of weight and realism in their reactions and motions. The story of a young man trying to make an impact on the world without cause, a boy who grew up too soon, and the inconoclastic hobo girl that helps them both sort their lives out.
Jimmy Corrigan, by Chris Ware -- a meek, lonely man who is essentially a 30-year-old Charlie Brown gets a letter one day from his father, whom he's never met, setting off a long and colourful exploration of the effect fathers have on their sons.
Pretty much anything Daniel Clowes has ever done-- I love how his characters all feel like people you could actually meet, and he's not afraid to give them major flaws. He focuses on fictional slice-of-life stories with a knack for subtle details and well-paced character development. In a weird way, I also appreciate that there are very few conventionally "pretty" Daniel Clowes characters.
Blankets, by Craig Thompson -- One of the most elegantly crafted tales of the stormy seas and multiple facets of first love and heartbreak in comics.
Bone, by Jeff Smith -- I'm not usually much of a fantasy fan, so Bone wins extra points for winning me over in spite of it's genre. It balances it's humor and drama with careful precision for maximum impact of both, and crafts a world and culture that I wish would be returned to in another book. (There are a couple spinoffs, but they don't really expand on the setting any further.)
Anything of Ross Campbell's but especially Wet Moon (a college drama tinged with the supernatural), Water Baby (the story of a shark attack, a long annoying road trip, and a jerk ex-boyfriend), and Shadoweyes (Campbell's own take on the superhero genre, about a nocturnal mutant who looks something like a tiny blue xenomorph and is adorably enthusiastic about the whole fighting-crime thing).
Anything by Will Eisner, ever, seriously. The man knew his craft and you can learn a lot from him. I particularly recommend his Dropsie Avenue stories, available in a few reprinted collections.
Calvin and Hobbes, by Bill Watterson -- if you've never read this legendary comic strip, drop everything, right now, and do so. The older I get, the more of Bill Watterson's craft I see evident.
Bear, by Jamie Smart -- if Tom and Jerry were far more genuinely violent and thickly British, and were comprised of a world-weary, smart-mouthed teddy bear and a sociopathic, legitimately evil kitty instead of your standard cat and mouse, you'd get something like Bear. It's not particularly deep or fulfilling, but it's not trying to be. It's well-done silly, slightly crude fun that is, occasionally, actually clever, just to throw you off.
I Feel Sick, by Jhonen Vasquez -- While not as well known as the author's breakout works JtHM and Squee, as well as his still-ubiquitous cartoon series, I consider this brief little two-issue pair to be his strongest work. Technically a spinoff from JtHM, the story itself gets across the same major themes as its parent work in a far more condensed, succinct form that suffers far less of the former's pretentiousness. The beginning of issue 2 is a bit too whiny, coming from the perspective of someone who is in a similar job situation, but apart from that its all gravy.
Black Jack, by Osamu Tezuka -- a medical drama as only Tezuka could bring you. One of the early stories involves a psychic tumor, just to give you an idea.
The Filth, by Grant Morrison -- A story about dimension-hopping garbage men, who are also assassins, whose targets are not actual human beings but humanoid beings designed to disrupt the flow of reality--and the whole thing is a metaphor for the functions of the human body. Is every last bit as weird as it sounds.
WE3, again by Grant Morrison -- What you get when you crossbreed Homeward Bound with a mecha series. A surreal cautionary tale about animal rights that manages to avoid being preachy or wagging a finger at humanity as those sorts of stories are wont to do. It's also an all-too-rare case of "realistic" feeling animal dialogue.
Watchmen and V for Vendetta, by Alan Moore -- Classics. Read 'em both. These two are known enough that I don't think I need a descriptive blurb. And trust me, while the film adaptions aren't terrible...read the books first if you can. Just do it.
The Sandman, by Neil Gaiman -- Another well-known classic that (probably) needs little-to-no introduction here. Neil excellently weaves a work of modern mythology, while incorporating history's own established mythos into it.
Transmetropolitan, by Warren Ellis -- The long, satisfying battles of an atrocious person (who happens to be a journalist) in a city full of even more atrocious people (in a future where almost nothing is taboo). Gleefully offensive, yet intelligent.
Widgey Q. Butterfluff and Pepper Penwell, by Steph Cherrywell -- smartly-done deconstructive parodies of, respectively, cutesy Saturday morning 80s cartoons and Nancy Drew-esque tween mystery novels.
The Four Immigrants Manga, by Yoshitaki "Henry" Kiyama -- Entirely unlike the sparkly-eyed newsprint tomes you've no doubt come across in every bookstore. Four Immigrants is a straight-up historical document, detailing a humorous but matter-of-fact account of the lives of Japanese immigrants in 1920/30s New York. Though the vast majority of the jokes are entirely lost in the translation, it's still fascinating just because of the person and time period it came from. Kiyama wrote all the Japanese dialogue in his first language, and wrote characters speaking English in English. Tthe translation compensates for that beautifully, while giving a sense of immersion to the reader--the Japanese is replaced with typed, neat English, while Kiyama's rough-handed and grammatically wobbly English remains for characters speaking English, to really give a sense of being someone in a new country--your own language is perfectly understandable, but when talking to locals you might only catch a few important words and worry about your own speech coming out stilted and awkward.
Safe Area Gorazde, by Joe Sacco -- A sort of comics-form war journal of the Bosnian War. It was very interesting for me to read about, as I had grown up during that time but heard nothing about said war until many years later. May be a bit dry for some, but for people who like modern war accounts, it's a must-read. (I'm not a big war buff myself, but it won me over regardless.)
Epileptic, by David B. -- The author's rather surreal account of growing up with an older brother with severe epilepsy.
Wonton Soup, by James Stokoe -- Stokoe brings a gleefully frenetic energy to a story that's one-part Star Wars, one-part Iron Chef, one-part classic action manga and one-part stoner flick. Seriously. It's self-billed as a space trucker cooking opera. How could that NOT be awesome? Stokoe has another, fantasy-rooted series I want to check out soon, called Orc Stain. It is, appropriately, about orcs.
Understanding Comics, by Scott McCloud -- An oft-cited work, and for good reason. While McCloud's textbook isn't the absolute best resource on comics theory (yes, that's a thing) out there, it's a very good starting point for anyone looking to study it. His follow-up book, Reinventing Comics, is...not recommended and what most people are thinking of when they make fun of Scott McCloud. The third book, however, Making Comics, is a decent basic resource that draws a lot on the first book.
Sam & Max, by Steve Purcell -- Before it was an (awesome) video game series, and for a while during it, Sam & Max, the tale of an inexplicably humanoid dog and a "hyperkinetic rabbity thing" that dub themselves the "Freelance Police," was a comic. Several comics, actually, made at various intervals over the course of several years. It's self-aware in all the best ways, cartoony as can be, and perfectly okay with that.
Likewise, by Ariel Schrag -- The fact that Schrag started her massive, ambitious comics projects when she was so young makes me exceedingly jealous. From middle school on, she began to chronicle frank accounts of her life in comics form, and continued all through high school--her personal diaries, really, that she has chosen to share with the world. Likewise, covering the latter half of her high school years, is the only one I've read but I'd like to pick up her others. Due to various writing quirks, as well as the fact that she doesn't bother to edit how shaky her handwriting gets when she draws a panel while crying/upset (something I appreciated, as it adds to the raw adolescent emotion that this work absolutely bursts with), it can get a little tricky to follow exactly what's going on sometimes.
The autobiographical comics of Jeff Brown and Julia Wertz -- Two more autobio-comics heroes, both similar--giving straightforward, well-delivered humorous anecdotes from their lives in a simple but relatable cartoon style.