Spoilers for Cowboy Bebop ahead:
Cowboy Bebop is a 1998 single season anime that teaches the viewer about friendship, love, and the struggle of life. In the anime, we follow a cast of characters, Spike, Jet, Faye, and Ed, on their journey through near-earth star systems working as bounty hunters to chase their next meal.
The central theme of Cowboy Bebop is "finality". The finality of death and the irreversibility of time, and the fundamental flaws in the ones we love. Each character brings a unique backstory and each backstory teaches us a lesson.
Edward - The Failures of Those We Love
Towards the end of the show, we meet Ed's father. He has been travelling around earth looking for her (but mainly chasing meteor crashes). The gang manages to track him down, reuniting Ed with her father. Ed's father immediately asks her to stay with him, but just as quickly goes off chasing the next meteor landing, abandoning Ed for the second time (that we know of) in her short life.
Ed's perpetual sunny disposition leading up to this point in the show can be viewed from a new perspective. She was taught time and time again by her father that people will fail you, that they won't live up to their promises - and we can understand why Ed never seems to be upset when Faye lies to Ed and fails to live up to her promises to Ed.
Faye - You Will Never Get Back What is Gone
Faye Valentine, a debt-strattled amnesiac with a knack for inconsistency. What Faye initially projects as a deep secrecy about her past is eventually revealed to be the result of a complete loss of her childhood memories waking from a life-saving stasis she entered after an unnamed life threatening accident. (It is implied that this accident is the same event that destroyed most of Earth, separating it from the rest of the human-settled star systems.)
The team recovers video footage of Faye as a child, recording a message to her "future self". Seeing the footage, Faye is inspired to find and return to her place of birth. Upon her return, Faye discovers her childhood home's crumbled remains and sees firsthand that everything from her past life is completely and irrevocably obliterated.
Spike - You Suffer Until You Die
Spike is portrayed as a walking paradox. He continually throws himself in deadly situations, wishing for his own demise, yet seems to be invulnerable to the only thing he really wants in life. The whole story hints at how his life is lived simply so he can find Julia again but we know that he could have gone out and found her if he had really tried. What Spike was really looking for was death. He knows he will never get to live the life he once almost had with Julia. Every day he seeks death and never finds it.
In the final episode, Spike gets his wish. Julia is dead and he can face his rival, vicious, once and for all. The two of them know that their lives are charmed and they are the only ones alive capable of killing the other. In the end, they do. Each suffered through life and was given the reward we are all guaranteed after our struggle.
Jet - Eventually, You Lose It All
Jet's tragedy is the most hidden of the four, but the most relatable to the everyday person. The show ends with Spike dead, Ed chasing her father, and Faye alone and facing the erasure of her life. And we don't see Jet. The ex cop who had the love of his life run out on him through no fault of his own. The only friend he has had in the past decade killed after a short 3 years of brotherhood. At the end of Cowboy Bebop Jet is alone and he most likely will never find another friend like Spike.
Spike found death, Faye saw closure, Ed has her father to chase, but Jet - Jet has nothing to live for.