The Optimist: TK, being too innocent to know how bad things can get.
The Realist: Izzy, too smart for blind optimism.
The Cynic: Joe, who expects everything to go wrong; the dub team took the opportunity to make him a Sickly Neurotic Geek.
The Apathetic: Mimi, who is uncomfortable and wants to go home now, the fate of two worlds be damned.
Digimon Adventure 02: TK (the Realist), Davis (the Optimist), Kari (the Realist), Yolei (Optimist & Conflicted hybrid), Cody (Cynic & Conflicted hybrid), and Ken checks in as the Realist.
Digimon Tamers has Takato (the Optimist), Rika (the Cynic), Henry (the Realist), Jeri rotating between Conflicted and Optimist, and the Apathtics Kenta, Kazu (in the "just tagging along" sense), Suzie (in the "whole different motivation" sense, basically a little girl's whims) and Ryo. (in the removed/enigmatic/different background sense)
Digimon Frontier also gives us Takuya (the Realist), Koji (the Cynic), Zoe (the Optimist), JP (the Apathetic), and Tommy and Koichi (both the Conflicted).
Guy is The Cynic. World-wise, snarky, and used to fending for himself, Guy has the most negative outlook of the bunch, and by far the most callous way of handling things (mostly due to his unpleasant history).
Etienne is The Optimist. Gentle, optimistic, and loving to anyone and everyone Etienne doesn't have anywhere near as negative an outlook as his friends. He perpetually sees the best in everyone, and is much more willing to accept change.
Nicolas is The Realist. Somewhere in between Guy's negativity and Etienne's boundless empathy, Nicolas is a stickler for the rules, and determined to be the kind of knight his society demands.
Micheal is The Apathetic. Strange, seemingly ditzy, and definitely playing by his own rules, Michael's bizarre sense of morality doesn't even resemble that shared by the rest of the group. His outsider status cements him as this.
Haruka Kotoura: The Conflicted Up to Eleven; She fits every part of the description almost too well.
Yoshihisa Manabe: The Optimist; cheerful guy with a passion to protect Haruka (his girlfriend) and sees many things in a very unusual, yet loving way.
Hiyori Moritani: The Cynic; very rough and antagonistic with huge vices for things and people that don't sit well with her, doesn't play by the rules, and is sometimes thuggish.
Yuriko Mifune: The Realist; grounded in facts and is unconventional in utilizing them, cares about her goal and eventually learns to care about the people around her, and open to possibilities.
Daiichi Muruto: The Apathetic; consistently neutral outlook, doesn't show biases, often aloof and on the sidelines, plays along but is more of an observer.
Lucky Star: Tsukasa (the Optimist), Kagami (the Cynic), Miyuki (the Realist) and Konata (the Apathetic).
Lupin III: Because Goemon and Jigen trust Lupin so much, we rarely see all the characters together demonstrating the conflict. Usually it's just the two of them sniping at each other when Lupin is absent.
The Cynic: Jigen is a soured realist whose hazy past is best left unspoken.
The Optimist: Goemon is often contrasted with the other men by his naivety.
The Realist: Lupin is generally able to figure out some way to do things that no one else had been able to think of. This trait, as well as his ability to balance the cynicism and optimism, is what keeps his allies around.
The Apathetic: Fujiko has probably already betrayed the group at this point, and about to beg Lupin to forgive her. Even the Optimist knows she'll betray them again.
One Piece: right at the beginning when there were only 4 members, it was Usopp (the Apathetic), Luffy (the Optimist), Zoro (the Cynic), and Nami (the Realist).
Princess Tutu, Kraehe (the Cynic), Princess Tutu (the Optimist), Fakir (the Realist), Mytho (the Apathetic or Conflicted).
Puella Magi Madoka Magica: Kyoko/Homura (the Cynics), Mami Tomoe (the Realist), Madoka is mostly the Conflicted (or Optimist when she is magical girl), Sayaka (the Optimist), and Kyuubey (the Apathetic).
Rurouni Kenshin manages to have the main characters fulfill all the roles at different times: Kaoru (the Optimist), Kenshin (the Realist), Yahiko (the Cynic), and Sanosuke and Megumi (the Apathetics).
Yet frequently, Sano (Cynic), Megumi and Yahiko (Realists), and Kenshin (Optimist). Kaoru, Kenshin, and Megumi all show signs of the conflicted as well.
When others join the main cast: Saito (the Cynic), Misao (the Optimist), and Aoshi (the Apathetic).
Saiyuki has Sanzo (the Cynic), Goku (the Optimist), Hakkai (the Realist), and Gojyo (the Apathetic).
Luke and Millina, Zelgadis and Amelia's replacements in the original book series, are both the Apathetic.
Tengen Toppa Gurren Lagann (Early episodes): Simon (the Cynic), Kamina (the Optimist), Yoko (the Realist), Leeron (the Apathetic).
Later it becomes: Simon (the Cynic), Nia (the Optimist), Yoko (the Realist), Leeron (the Apathetic).
At the beginning of season 2 is was: Rossiu (the Cynic, Kittan (the Optimist), Simon (the Realist), and Viral (the Apathetic); then it turned into Gimy (the Cynic), Simon/Kittan (the Optimist), Leeron/Yoko (the Realist) and Lordgenome (the Apathetic). Maybe.
Tokyo Majin: Koyuichi (the Cynic), Aoi (the Optimist), Kisaragi (the Realist), Tatsuma (the Apathetic) and Daigo with Sakurai (the Conflicted)
Trigun: Wolfwood as Cynic, Vash as Optimist, Meryl as Realist, Milly as Apathetic or Conflicted.
Tsubasa -RESERVoir CHRoNiCLE-: Kurogane (the Cynic), Sakura (the Optimist), Syaoran (the Realist), Fay (the Apathetic), and Mokona (the Conflicted).
Weiß Kreuz: Aya (the Cynic), Ken (the Optimist), Yoji (starts off the Realist; becomes the Conflicted), and Omi (starts off the Conflicted; becomes the Realist).
Wolf's Rain: Kiba (the Realist), Tsume (the Cynic), Hige (the Apathetic), and Toboe (the Optimist).
The Humans make up another four as well: Darcia (the Cynic), Cher (the Optimist), Hubb (the Realist), and Quent (the Apathetic).
YuYu Hakusho: Hiei (the Cynic), Kuwabara (the Optimist), Yusuke (the Realist, though sometimes a lighter Cynic), and Kurama (the Apathetic).