Spider-Man embodies this trope to the point of deserving to have it named after him. Though really, he spends a lot of time in incredibly-energetic-snarker mode too. At one point, this embodied him so much, a lot of people used to call them "Spider-zingers".
Played with by Spider-Man 2099, who's terse and straightforward in costume, but a killer snarker in his civvies.
His snarkiness is well known even in-universe. In an issue of Excalibur, the members of the Wrecking Crew briefly mentioned Spider-Man's name, elliciting a "I hate Spider-Man" from one of the members. The response: "Everyone hates Spider-Man."
In the Secret War miniseries, Spidey met Black Widow out of costume and made a quick joke. Widow suddenly realized who she was speaking with.
Batman: Jim will pull through! Alfred: Or what, master Bruce? You'll dress up like a giant bat and haunt the night for the rest of your life?
Whenever Batman (in any incarnation) isn't either moping around in Wangst or being The Comically Serious, he's generally the one with a deadpan line. Or, as Jaime Reyes (Blue Beetle III) put it, "Batman's actually kind of funny, in a dry, scary way." Typically, Batman needs Superman as a foil if he's going to be funny.
The Robins (most of them) tend to pick up the slack as far as snark goes.
John Byrne's character, Rog-2000, does this often.
Crook: Cheese it! The Coppers!
Rog (As crook's knife shatters on his chest): I'm not copper! I'm 100% Stainless steel, see?
In contrast to Spidey, Clark Kent tends to be quite snarky at the Planet, but drops it as Superman. This is Depending on the Writer — in the Movie, Superman was at least as snarky as Spider-Man ever was.
It often depends who he's talking to, as well. When he's "Superman", say in public, or against a villain, no snarking. When he's around somebody that knows the real him (Clark), like Batman, he tends to be more snarky.
Hellboy often uses deadpan. His Catch Phrase "Ah, Crap," can be said to be an example, as is his habit of yelling "Boom!" when he punches someone with the Right Hand of Doom.
Elaine Belloc from Lucifer has occasional moments of deadpan snarking, most notably when she sat at the table with Archangel Michael, Lucifer and Destiny of the Endless debating heatedly. Her comment was: "Another glass of testosterone, anyone?"
Gryph:(upon being levitated by Zayne) I seem to have lost weight. (reading the news report on Zayne's escape:) Gryph: "... Failed Padawan..." "... Slew classmates..." "Fugitive is armed and..." Umm... Zayne: Dangerous? Gryph: No. "Deranged." Well, that certainly sounds like you.
The bulk of the characters in Star Wars: Rebellion volume 2: The Ahakista Gambit have one or two smart remarks, but Baco Par, the Snarky Non Human Side Kick is notable in that he barely has ten lines which aren't snarky. See the quotes page.
Every single member of the Young Avengers displays this to some extent. They beat up about one enemy for every ten lines of snarky dialogue and Witty Banter.
Black Bolt from the Marvel ComicsThe Inhumans is The Voiceless; if he were but to whisper, it would unleash a shockwave strong enough to destroy a city. Despite this, he's constantly thinking such lines. During his time with the Illuminati, fellow member Charles Xavier doubles as a translator. Also, when he wants to declare war, well, he doesn't beat around the bush: he declares "War."
The Illuminati miniseries has a very funny part where Black Bolt comments that his wife (who speaks for him) never lets him get in a word edgewise.
Everyone says lines like that in any book involving Deadpool.
Sonic is incredibly snarky in his comic series. During one battle with the near omnipotent Enerjak, Sonic makes several puns on the name. When Enerjak immobilizes him with chaos energy and asks if he's quite finished with the witty remarks, Sonic makes seven or eight more cracks in rapid succession, before Enerjak hurls him through a wall.
X-Men: Gambit (to name just one) is the absolute King of this trope. Every other sentence that comes out of his mouth is a snark. And you can never tell when he means it...
Suprisingly, Cyclops is quite snarky when he wants to be as well. In the First Class comic for example:
Matt Fraction's 26 issue run on Punisher War Journal gave frank a sort of dark, subtle sense of humor.
Punisher: Nobody gets me. Maybe it's the skull.
Denny O'Neil and Greg Rucka's versions of The Question, although as Vic Sage he tends to combine this with Jerk Ass.
According to the Author's Notes, this was deliberate in regards to Renee Montoya in 52. When she's out of the mask she's serious, angtsty and often quite brusque, when she's The Question, she starts to snark and make jokes. Not well, but it shows how she can become someone else.
Flash Forward/Negative Man II of the Doom Patrol. His nickname is an in-joke referencing the fact that there was a "Negative Man" in the original Doom Patrol — that, and the fact that he's extremely hard to get along with due to his icy personality and seeming inability to say anything nice about anyone.
This is such a defining characteristic of Lenny from Shade, the Changing Man that when her ability to snark was stolen (along with her sex drive,) she attempted suicide.
Doctor Strange on occasion. His manservant Wong is pretty good at it too.
The Savage Dragon does this both on and off the job. Sometimes, he takes it far enough that people consider him a Jerk Ass at times.
A newspaper comic example: When Garfield began, Jon Arbuckle was the original snarker (being most notorious during the fall of 1978), with Dr. Liz Wilson taking that role when she was introduced the following year. (Jon by the turn of the eighties was yet the Straw Loser for he is known today). Finally, by the mid-1990's the cast had been reduced to Garfield, Jon and Odie (apart from the unseen Ellen and Jon's various blind dates), and the fat cat took the deadpan persona he is today.
Eva Kant from Diabolik has her moments. Her favourite snark is insisting her husband's death (devoured by a panther) was an accident, as he was trying to set the panther on her, and Eva didn't mean to set the panther on him.
Wilq the Superhero, the main protagonist of a Polish comic series of the same name, is so sarcastic that he was actually called "the most frustrated character of Polish comic books" by the Wprost magazine.