Conflicted: Hawke oneself takes this role — a Sad Clown who tries to maintain the peace in Kirkwall and amongst the companions, but often lets desire for stability prevent him/her from being more proactive.
Anders straddles the line between Cynic and Idealist, being a Well-Intentioned Extremist who combines self-sacrificing loyalty to his ideals with hostility and ruthlessness.
Ever17 female cast: You (the Optimist), Tsugumi (the Cynic), Sora (the Realist), and Sara/Coco (the Apathetics).
Everworld — Jalil (the Cynic), David (the Optimist), April (the Realist), Christopher (the Conflicted), and Senna (something of the Apathetic).
All of the opposing and antithetical factions in Fallout 4:
The Optimist: The Minutemen, as their original goal was to protect settlements out of good will but they were nearly wiped out after a string of bad luck. They can make a comeback and they are even more idealistic than ever despite all the shit they've been dragged through. They're flexible on policy when it comes to the Synths.
The Cynic: The Institute, as they believe that it is futile to allow the Commonwealth to continue existing and want to start anew in a new society underground. However, the same people they claim to want to help fear them due to many of their own actions. To them, the Synth is Just a Machine.
The Apathetic: The Railroad views the Synths as living, thinking beings worthy of respect, and wants to liberate all Synths from the Institute. The problem is that this is their only goal and they don't really care about anyone else in the Commonwealth.
The Realist: The Brotherhood of Steel. Ten years after the war with the Enclave, the original teachings of Elder Lyons have been lost since his death and the death of his daughter, Sarah Lyons. Arthur Maxson is in charge and wants to try and expand into the Commonwealth to oppose the Institute. To them, Synths are abominations against technology and to be destroyed down to the last.
Half-Life 2: Barney Calhoun (the Cynic), Alyx Vance (the Optimist), Dr. Kleiner (the Realist), and Dr. Mossman (the Apathetic).
The first Knights of the Old Republic: Carth's a Cynic. Mission is very much an Optimist. Canderous is Apathetic (a Mandalorian on a boatload of Jedi and Republic sympathizers, and has nothing better to do). Bastila looks like a Realist, but is actually Conflicted. Juhani appears Conflicted, but bends more Realist. Zaalbar is also Conflicted (you can influence him to the Dark Side pretty easily). The droids are Apathetic (T3 hasn't lived long enough to develop a personality; HK-47 just wants to shoot things for the meatbag in charge). Jolee likes to ride the line between Cynic and Apathetic.
Left 4 Dead: Francis who hates everything (the Cynic), hopeful Louis (the Optimist), Bill the experienced (the Realist), and, knowledgeable on zombies, Zoey (the Apathetic).
Left 4 Dead 2: pessimistic Nick (the Cynic), naive Ellis (the Optimist), Coach as leader (the Realist), and Rochelle, the only neutral character (the Apathetic).
The Legend of Dragoon. Dart is the Realist, Lavitz is the Optimist, Rose is the Cynic, Shana is the Conflicted. Haschel later joins as the Apathetic. This setup holds from the time Rose joins all the way until Dragoon's It Was His Sled moment happens, where it transitions into a proper Five-Man Band.
Mega Man X'' — the Maverick Hunters, Commander, Mission Operator, and mechanic in X5-X8:
Realist: Signas — the mediator who always admires X's pacifism, but always realistic about the need to fight for peace and justice.
Optimist: Douglas (X5-6), Axl (X7-8) — the former as idealistic and confident, although this is not expanded on; the latter seeks to rectify the wrongs of his former affiliation and believes he can take on the world.
Apathetic: Alia — the Mission Operator, Computer Specialist and Navigator in the series, less in-story involvement otherwise.
Conflicted: X — Willing to fight for peace and justice at first, but a pacifist paranoid of breaking the first robotics rule (not to harm a human), then temporarily retires and reluctant to let Axl become a hunter.
Mega Man Zero — Counting the 1st game's Four Guardians and the four bosses in the 2nd's "Chase Elpizo" mission (three of them the same, totaling five).
Cynic: Phantom — out of fierce loyalty to Master X (a copy, rather), seldom thinks about anything besides antipathy toward "Mavericks" and, therefore, resorts easily to drastic Anti-Hero measures of explosive-detonation, for instance the factory in the first game.
Realist: Fefnir — mostly just a competitive Blood Knight into defense as a Guardian for the fun of it, a lot like Leviathan, but a more encouraging character.
Optimist: Burble Hekelot — does his job of protecting a Neo Arcadian forest very faithfully; driven least by selfish, prideful motives and farthest from Anti-Hero of all of them, besides Harpuia.
Conflicted: Harpuia — sense of honor and most merciful of all like an Optimist (and does Guardian tasks for only the right reasons, contrasting Leviathan), yet still not easily trusting of anyone on the opposite side of the conflict; often pondering when to lean more to Cynic or Optimist in many situations.
Metroid Prime 3: Corruption: Rundas (the Cynic), Samus (the Realist, sometimes Conflicted), Gandrayda (the Optimist), and Ghor (the Conflicted, sometimes Apathetic).
The boys in Nameless: Lance (the Cynic), Red (the Optimist), Tei (the Realist), Yuri (the Apathetic — he does care but either expects things to work themselves out or acts without consulting the others) and Yeonho (the Conflicted).
Nazi Zombies: Tank (optimist), Takeo (realist), Nikolai (apathetic), and Richtofen (cynic).
The crash survivors from Remember11: Kokoro (the Optimist), Mayuzumi (the Cynic), Yomogi (the Realist) and Yuni (the Apathetic).
Sly Cooper: Sly (the Apathetic/Realist), Bentley (the Cynic), Murray (the Optimist), Carmelita (the Conflicted).
The Star Fox team. There's Falco (Cynic), Slippy (Optimist), Peppy (Realist) and Fox (Conflicted). When Krystal replaces Peppy in later games, she fills the Conflicted spot with Fox becoming more of a Realist.
This actually becomes a gameplay mechanic in This War of Mine when it comes to emotion levels; The Optimist is much more eligible for mood swings than The Cynic, and the more emotional characters are better at curing depression.
The Realists: Marko, Pavle, Katia
The Cynics: Roman, Bruno, Emilia
The Optimists: Zlata, Boris, Cveta
The Apathetics: Marin, Arica, Anton
The playable characters of the Touhou Project: Reimu (the Cynic), Marisa (the Realist), Sanae (the Optimist), and Sakuya and Youmu taking turns being the Apathetic.
Four of the major characters that you meet and (potentially) befriend in Undertale can fit this dynamic. In the order you meet them: Sans (the Apathetic), Papyrus (the Optimist), Undyne (the Cynic), and Alphys (the Realist). Different sides of this dynamic show depending on how you play.