In The Gamers Alliance, Marya finally cracks when she becomes guilt-ridden by all the bad things she's done and commits suicide in order to atone for her sins and be reunited with her husband Kagetsu in the afterlife.
Germaine from Neurotically Yours attempts suicide fairly regularly. In one of earliest episodes, she stands with a gun to her head while Foamy relentlessly mocks her lack of resolution and reasons for putting the gun to her head. It's implied that she ends up shooting Foamy. "Almost Serious Suicide".
In a later episode, the suicide helpline guy mocks her for using suicide helplines so much.
A good chunk of Sailor Nothing derives dramatic tension from a "will she or won't she" situation, especially when it's revealed that every Sailor to ever be in Himei's position ended up killing herself.
Many characters in Survival of the Fittest choose to commit suicide rather than kill their classmates or allow themselves to be killed. The most memorable of these is probably River Garraty, who was the first one to kill themselves by intentionally running into a danger zone. In v3, there have been six intentional suicides; Tegan Bianco, Keiji Tanaka, Anna Grout, Bobby Jacks, Gabe McCallum and Quincy Archer. Three other characters killed themselves by accident.
Recently in v4, Dawne Jiang commits suicide by remaining in a dangerzone after it has been announced as such. Hermione Miller and Violetta Lindsberg also commit suicide by pulling on their collars.
Maria Graham attempts suicide by trying to slash her own throat with a shard of broken glass. Fortunately, one of her friends shows up just in time to stop her.
In the web-novel Fragile, Severin has an irrational fascination with the idea of suicide after going insane and is found at the end attempting to slit his wrists; or at least, Page thinks he is, but he finds Severin before anything can be done. It's never stated exactly why, but it might be because he's attempting to escape the pain of being insane.
Jerry at the end of Jerry. The rest of the series elaborates on his backstory and shows how the other characters were affected by the event.
The Nostalgia Critic takes special precautions to prevent himself from committing suicide when reviewing Batman & Robin. Even so, he still sneaks in a cyanide pill and takes it during the review. Someone promptly runs on camera and performs the Heimlich Manuver so he survives.
In many other reviews, after a particularly bad scene, he pulls out a gun and shoots himself in the head, and goes back to reviewing three seconds later.
When Spoony sends Critic a copy of Reb Brown's Captain America film, Critic hangs himself rather than watch the film.
And during The Pebble and the Penguin, he goes to take a bath and brings his toaster with him.
Another critic on the site, Film Brain, sometimes places a gun to his head when things are getting to be too much for him. "Why is it always empty?!"
The Nostalgia Chick pulls a plastic bag over her head and strangles herself after being subjected to "There Must Be An Angel".
Todd In The Shadows has also killed himself with a grocery bag ("BedRock"). He's also beaten himself to death with a book ("Whatcha Say") and committed seppuku ("Like a G6"). He's put a (toy) gun to his head or under his chin a few times as well.
One of the authors on Newgrounds made a suicide. Irony of that his first submission to Newgrounds was... Fun With Suicide!
General Briggs in the final chapter of Broken Saints.
According to Bowser's Kingdom episode 10, Lemmy Koopa was driven to suicide because of a mediocre review of the show.
Hal: Hmm, well let's check out this review.
Jeff: Lemonater said it was good, but need plot and character development. It was good, but it's not the Fresh Prince.
Hal: Little did we know that poor Lemmy idolised the Fresh Prince. He's always tried to be like Will Smith and tried his best. He was good... just not Fresh Prince good. *sighs* I miss you Lemmy... *sniff* I miss you...
Shot of Lemmy hanging himself.
Toad is driven to suicide at the end of talk my head off because he killed so many people.
In The Guild, Zaboo tries to hang himself with an ethernet code to escape his overbearing mother (no screenshot, but it happened). This ends up being the killing blow for her. Not that she actually dies, it's just in their fantasy of her as a monster...It Makes Sensein Context.
Look To The West: Lavoisier offs himself when he learns that the primitive gas chamber he built has been used to execute the French Royal Family.
The Spy, from Water Human, chose to throw himself off a cliff rather than let the Water-Human kill him. In fact, he did this mostly because he was so depressed by how people seemed to constantly die in droves while around the Water-Human.
The Original Spoony One came back from the dead in the Final Fantasy X review. He was ready to kill his clone in order to get his show back. After the clone just gave up the show, Original Spoony realized that he had to review Final Fantasy X. He promptly shot himself in the head and became dead. Again.
A Magical Girl attempting this by jumping on Live National TV is what starts off the Magical Girl Alliance. But she gets better.
After two minutes of attempting to play the legendarily broken Big Rigs: Off the Road Racing, Gamespot reviewer Alex Navarro goes outside and lies down on the driveway, presumably in hopes of being run over by an oncoming car.
This has happened Toki so many times, once in Insanity and Resentment and, before that, possibly, she tried to get herself runover by a car in Flashbacks I (no one knows her real motives and Toki may never tell them, though, she could have been leaving to die in peace but, at that point, getting runover with a car would most certainly prove fatal). Both are understandable because, in the first one, she is mentally ill and, the latter, is because she is really sick with leukemia and was being abused and negelected at the time (in conjunctions with the fact that she in the later stages and is virtually dying). Neither has anything to do with her heritage.
In Vs. episode 5, while playing Cartoon Network: Punch Time Explosion, he allows his character, Captain Planet, to fall down a hole, after he found out his special attack ended with an explosion of rainbows and hearts.
In Let's PlayMinecraft episode 45, he questions if they have to hop through a circle hole. Ray corrects him by saying it's a square hole. Jack hangs his characters head down and throws him into the lava pit nearby.
In Dragon Ball Abridged, In Future Trunks's timeline, Yamcha does this when he finds out Bulma got pregnant with Vegeta's baby. Goku is attempting to prevent it in this timeline by reminding Yamcha they're friends. Given the source canon, it's presumed he succeeds.
