Frasier/Heartwarming

In the episode "The Gift Horse", Martin says that Niles' birthday gift of his old police horse was the best gift he could get. After he thanks him, Niles lies and says that the horse was from both of them.
Another one in the episode "The Maris Counselor" when after Niles breaks it off with Maris for good, the three Crane men have drinks and joke about their failed love lives. At one point in the discussion, when Niles is explaining how he ran into Maris's lover, there is also a Crowning Moment of Funny:

Niles: Fifteen years with Maris, I end up in bed with her lover.
Martin: Gee, I didn't need to hear that!
Niles: No, no, it was an accident. It was pitch dark, I thought he was Maris.
Frasier: It's a natural mistake. What tipped you off?
Niles: The heat from her side of the bed. [they all laugh]

'The Proposal' generally is pretty heartwarming but especially Frasier's reaction to it as he watches it in secret and then proceeds to tackle the trumpet guy to preserve the silence.
The ending of Crock Tales, when everyone comes home to dinner, and Frasier reconsiders the broken crockpot not as garbage, but as a silent observer to all the precious moments Frasier had spent with his family over the years.
In 'Enemy At the Gate' Frasier refuses to pay a parking fee because he hasn't actually parked so he decides to stay his full 20 minutes and holds up traffic behind him. Niles become fed up and is about to leave until the man working there calls Frasier an idiot. Niles says Frasier is just passionate, looks at him through the window and then sits back in the car. The brothers share a respectful look.
Martin thanking his son "for everything" in the finale.
The episode when Niles has heart surgery. During the episode Niles almost out of his head on anaesthetic muses that hospitals have memories and there are flashbacks throughout the episode to other times the characters were there at different points in their lives. After Niles recovers, Daphne goes to awaken Niles and as she leaves him it pans to a room where Daphne and Niles are welcoming their second child. It should be noted that the flashbacks are done like the hospital remembering actual events.
- Not to mention that fact that Niles' possibly-last words are, "Daphne, Daphne, Daphne," because he wants to say her name as much as he can.
Soon after finding out she's pregnant, Roz breaks down and cries because she's not sure she can raise a child on her own:

Frasier: But you're not alone, Roz. I'm here.

In a season 1 episode, Niles and Maris's marriage is in trouble for the first time, and Niles and Daphne are stuck alone in the mansion during a storm. Niles is about to make a move when a music box he bought for Maris springs into life:

Niles: It hasn't worked like that in years! Oh, Maris will be thrilled! [[[Beat]]] ...Maris.
Daphne: You really love her, don't you?
Niles: ...you know, I do.

- Slightly undercut by knowing that their marriage will break down in another year or so, but it's a sweet moment all the same, especially when Niles goes on to reassure Daphne that she'll find a man worthy of her "as soon as the gods create him."
In one episode, Roz has recently broken up from a long-term relationship and seems, to Frasier's concern, a little too okay with the whole thing. In the mean time, they're doing a show in Spokane to try and get more listeners but are having a hard time getting people to call in. Frasier asks Roz to pretend to be a caller and she randomly picks a fear of the dark as her psychological problem. However as Frasier pretends to analyse her problem, it swiftly turns into an analysis of her failed relationship and she starts to break down and cry. Frasier dispenses some touching advice, including a strong urging that she let her friends help her, and as soon as the "call" ends, he immediately gets up, runs over to her and gives her a big hug. Awwww.
- Undercut when Kenny races in to remind them that there's dead air. However, the heartwarming continues when callers, who hated Frasier for replacing a local legend, call it to comfort Roz, and a caller calls in with the same problem as Roz - Frasier's first legit call at the new station.
Near the end of season five a now single Niles decides to ask out Daphne, but loses his nerve and ends up telling her he's in love with a woman he made up. One thing leads to another and Daphne ends up helping him cook a romantic dinner for "Phyllis". As they start chopping up vegetables, Niles points about that they're chopping in rhythm. Daphne starts humming along to the beat, prompting Niles to start singing Heart and Soul. And then Daphne joins in.
- Subverted the hell out of in Daphne Returns, when Frasier accuses Niles of romanticizing Daphne too much. When they visit the scene, Frasier rolls his eyes, and snarks about it.

Frasier: Oh, please!
Niles: What?
Frasier: Even your everyday memories are idealized. How long until the cartoon blue bird lands on her shoulder?

Though the confession was made under a degree of duress, hearing Martin admit out loud that he loves his sons in Breaking the Ice was genuinely heartwarming.
In The 1000th Show, the city is throwing a huge party in Frasier's honor. Frasier spends half the episode trying to make it in time for the ceremony, facing one obstacle after another. As he's finally in a cab on the way to the park where the party is held, the driver starts telling him about his ex-wife getting remarried, and his relationship with his children. Frasier spends the remainder of the celebration sitting in the cab, right outside the park, listening.
In "Cheerful Goodbyes," Frasier says of his old bar pals:

"They were there for me when I needed friends the most."

In And the Dish Ran Away with the Spoon, Niles and Daphne seem not to be able to have their first date they looked forward to, but Frasier and Martin surprise them with organizing one.