Robot 13 from Gunnerkrigg Court is remarkably easy-going about his own well-being, taking the loss of his arm (and later, the loss of everything except his CPU) in stride. On the other hand, he becomes very distraught upon thinking that he hurt his "Mommy", Antimony.
Joyce of Roomies / It's Walky! took being a Pollyanna to new levels; Ignoring and/or avoiding anything that would put a dent in her rose-colored worldview (To the point where merely being forced to watch porn could break her mind. The argument could be made that Joyce wasn't a true Pollyanna as much as she was a different flavor of Love Freak.
Played with in Dominic Deegan. Gregory is probably the most cheerful person in the cast, despite the sheer amount of crap he's been through. But when he starts to form a new band, his soon-to-be bandmates call him out on this, and he lists some of the things he's been through. His bandmates are speechless.
Tavros from Homestuck. His life is pretty horrible all around, since he can't walk, his horns make it hard for him to sleep, his beloved Lusus (basically a cross between a parent and a pet) dies and the nicest thing anyone has done for him in the comic is cutting off his legs with a chainsaw so he can get a robotic pair. He's pretty happy despite all of this.
John, just... John.
EB: well to be honest, i never really believed any of your guys's doom and gloom nonsense.
EB: not because i think you are lying...
EB: i just feel like there must still be a way to win!
AG: That's the spirit, John!
AG: That is a winner's attitude, and there is always hope for someone who has that.
EB: yes, i agree.
EB: also, there is always hope for someone who has good friends to count on!
Even in the Post-Scratch universe, where he was raised by Betty Crocker/the Condesce. He even grew up to become a famous comedian.
Feferi. Not even being dead can diminish her spirit. Her friend Sollux (during one of his pessimistic phases) described her as "so ridiculously optimistic it's kind of sickening".
Oddly enough, Aradia. She starts off as an Emotionless Girl, but when she does regain the ability to feel, she becomes enthusiastically cheerful and smiles almost all the time. Even as her friends fight off killers in their midst, and she faces a near-omnipotent monster, she's convinced that there's no reason to grieve and that everything will turn out fine.
There's also John's grandmother, Nanna, who he definitely takes after. When she comes back to life after thirteen years of the afterlife, how does she respond? "HOO HOO". The same goes for Jane, her Alternate Timeline self, who took John's place as leader of his session, though she later turns into a deconstruction of what John would turn out to be like if he had to deal with the pressures she has to... which he eventually does, turning him into a deconstruction too.
Alice, The Medic from Dead Winter. You do see her get upset once in a while (for instance, when Trenton died), but she's the type to move on from bad things since being sad is just a distraction from her main drive, which is to help others.
Buwaro from Slightly Damned. His parents were killed before he was born, he was injured whilst in his egg and was born perpetually insane, and the only thing stopping that insanity is the pendant he always wears, he was abandoned alone in the Ring of the Slightly Damned for years, his sister was killed in their escape from hell, most people on Medius will try to attack him on sight and as a demon he doesn't get an afterlife. Despite this, he's still a loving goofball.
Of course, there's evidence that he wasn't just born insane, but also retarded. Leo retarded. His favorite game is throwing a large rock up and trying to catch it. It works out about as well as you'd expect, but he's still always cheerful.
The titular character in Equinox: Defender of The Horde. He is a silly Man Child who seems to see the world as a cartoony adventure. But throughout the story he faces death, betrayal, treason, and heartbreak, and while shaken to the bone at times with his experiences, he nonetheless manages to keep his optimistic childishness.
El Goonish Shive: Grace suffered years of trauma at the hands of Damien before being introduced. Although she reacted as anyone else would when it caught up with her, she has since become the most upbeat, positive character in the comic. However, this is strongly implied to be a facade; she's still a wreck underneath, and it sometimes shows.
Former Street Urchin Mia of True Villains is cheery and bright despite her Hilariously Abusive Childhood, and faces death, monsters, and powerful magic with a smile. She is also an Innocent Prodigy who is happy to make powerful weapons for Card Carrying Villains because they're her friends. More troublingly, she's also just as happy to help out with assassinations, and doesn't understand why fans of a woman she killed are upset because "So what? People die all the time."
Cameron from Luminary Children smiles gleefully as ever after seeing another girl get killed.
Nepta from tinyraygun still has a bright disposition after nearly getting blown up in space, crash landing out of hyperspace, getting robbed of all her possessions except the essentials, and having a baby alien tagging along.
Cucumber Quest's Princess Nautilus is relentlessly positive even in the worst situation, and sternly admonishes Cucumber for getting down over having to be the Legendary Hero. She even declares the power of positive thinking when they're confronted the Big Bad... although this nearly gets them both fried when he asks for a demonstration of their "power".
Hope from Alone in a Crowd is this along with Cheerful Child although it's revealed that she's no fool and is deliberately forcing herself to be happy in order to cope with a less-than-stellar home life. Even when her circumstances change, she keeps up the act in order to distract herself from the unhappy memories.