When Trish tries to apologize to Dante for selling him out to Mundus, Dante comforts her with his motto: "Devils Never Cry."
Trish: Dante, I... I... Dante: Trish, devils never cry. These tears? Tears are a gift only humans have.
Dante just seemed so happy that Trish was all right. In return, she practically glomped him in the ending.
Even in death, Eva (Dante and Vergil's mother) still watches over her children. She's the one who restored Trish to life, and gives Dante encouragement as he faces Mundus for the last time, as her spirit lives on inside the Perfect Amulet.
As Dante and Trish escape Mallet Island after Mundus's defeat, the surrounding sky clears up compared to the once-gloomy atmosphere that covered the setting for the majority of the story. Trish then looks up and is amazed by the view.
Trish: The sky! So clear! So blue! Dante: The sky is fair, and it will always be above everyone's head, no different! Trish: Like the sky, I feel like my heart is becoming clear...
Late in Lucia's disc, she is still distraught about her real origins, but Matier reassures her that the value of their history and experience is far greater than the circumstances of Lucia's birth.
Matier: Now, go. Everything that I know, I have passed on to you. You are my daughter. Lucia: Thank you, Mother.
Dante wiping away Lucia's tear and telling her "Devils Never Cry." when she volunteers to go on what may be a suicide mission, wishing to die like a human. And when it seems like he goes into Hell instead of her based on a coin flip, the end reveals it was heads on both sides the whole time. Even in this game, Dante's still a really great guy.
In an extra scene after the credits (by completing both campaigns), Lucia is seen in Dante's office, holding onto his coin and waiting for Dante to return. The prequel novel for 5, Before the Nightmare, shows that Lucia made repeat trips to Dante's office, hoping one day he''ll be back. Dante indeed does find a way out of hell and visits Dumary Island to reunite with Lucia. They hug and she cries in happiness.
Dante re-assuring Lady that he will deal with the whole mess caused by Arkham and Vergil. It's this moment where Lady is no longer hostile to him, and it's also a declaration of Dante's Character Development.
Dante: "Quite frankly, at first, I didn't give a damn. But because of you, I know what's important now. I know what I need to do....Trust me! I'll make things right for you. That's what my soul is telling me to do."
Followed by Lady offering Dante her Kalina Ann to aid him for the rest of his journey.
Lady: Dante! ...Please, free my father. Dante: I will, Lady.
Despite being serious at fighting/antagonizing Dante for most of the game, the aftermath of the Final Boss battle has Vergil conceding, then calmly warning his brother not to follow him down the Demon World, knowing full well that he lost the fight, and because the portal back to the human world is about to close. This single line of dialogue reveals he still has some concern for Dante's safety after all.
Vergil: Leave me and go, if you don't want to be trapped in the Demon World. I'm staying, this place was our father's home.
Dante crying over Vergil's apparent suicide/death... followed by Lady realizing that Dante doesn't want to explicitly admit it, and handles it tactfully with "somewhere out there, even a devil may cry when he loses a loved one," thus naming the series. Dante even replies with as close to an admission as it gets, with a "maybe". This line is also even more heartwarming in retrospect when compared to what happened beforehand during his fight with Vergil. His response to Lady's allusion of a crying devil is a sign of him admitting he's a Son of Sparda. Throughout the game, he refused to acknowledge his demonic heritage as well as his dad's place in his life. Now, he's finally accepting the connection, compared to moments prior when he spoke about embracing what his dad STOOD FOR even though he was a devil himself.
Dante: We are the sons of Sparda! Within each of us flows his blood, but more importantly, his soul!
Plenty of moments, from Dante dealing with/caring for Patty and the scenes between him and Lady and Trish. Probably the most heartwarming was the very end where Dante comes out alive after his battle with Abigail and everyone is just overjoyed.
The final scene of the series has Dante going off on a new job, then Lady and Trish ride along side talking about how it's first-come-first-serve, and they all playfully start an impromptu race down the highway. Then cut back to Dante's shop, and Patty has returned, lamenting how filthy the place still is, chiding Dante's laziness once again, before putting up a "Do Not Disturb" sign outside and gleefully starting to clean up, while a triumphant variation of the main theme plays, ending on a quick montage of the main characters doing stylish action moves, ending on a freeze-frame of Dante mid-slash.