Anytime we see how loyal Jeeves really is, or how much awe Bertie has for him.
The end of The Inimitable Jeeves, the first book in the Jeeves canon, perfectly establishes the emotional relationship between Bertie Wooster and his brilliant manservant. After one of Jeeves' schemes has left some third party under the impression that Bertie is insane for the millionth time that book, Bertie trudges home furiously with the intention of firing Jeeves. He storms in the front door and stops, suddenly overwhelmed by the atmosphere of comfort that Jeeves brings to his life. When Jeeves enters, Bertie tries to push through anyway, but just can't bring himself to out of sheer sentimentality.
I buzzed into the flat like an east wind...and there was the box of cigarettes on the small table and the illustrated weekly papers on the big table and my slippers on the floor, and every dashed thing so bally right, if you know what I mean, that I started calm down in the first two seconds. It was like one of those moments in a play where the chappie, about to steep himself in crime, suddenly hears the soft, appealing strains of the old melody he learned at his mother's knee. Softened, I mean to say. That's the word I want. I was softened. And then through the doorway there shimmered good old Jeeves in the wake of a tray full of the necessary ingredients, and there was something about the mere look of the man...
I would like to concur that I found that particular scene, as Jeeves might put it, "distinctly moving". To the point where I almost broke down crying, even though I was reading the thing aloud to a friend.
In the whole series, there is only one story narrated by Jeeves himself ("Bertie Changes His Mind"), which gives us some interesting insight into his motivations. Despite his plans this time aiming to keep Bertie from wanting children so as not to disrupt their "cosy bachelor establishment", he doesn't do it without some degree of remorse. When Bertie runs up to him in a panic and Jeeves informs him that the car has malfunctioned thus denying him an escape...
Jeeves: (narrating) I am fond of Mr. Wooster, and I admit I came very near to melting as I looked at his face. He was staring at me in a sort of dumb despair that would have touched anybody.
The entire second half of Thank You, Jeeves. Where to even begin?
Bertie and Sir Roderick Glossop do the "Enemy Mine" thing and find out that they have more in common than they thought. Pretty soon they're inviting each other over for lunch!
Jeeves rescues Bertie repeatedly despite the fact that he's no longer technically working for him (and therefore has no reason to), cumulating in a Crowning Moment of Awesome which leads to Bertie crying Tears of Joy and declaring, "Jeeves … there is none like you, none."
And finally, just when Bertie is feeling down about the fact that Jeeves is no longer his valet, Jeeves very humbly asks him if he can apply for the vacant position left by Brinkley, surprising Bertie so much that he drops a coffee pot. He's so moved and happy that he can't think of words to express his gratitude, cuing a Title Drop. If you aren't swooning with joy and/or grinning all over the place by that point, you really should be reading a different series.
Near the end of The Code of the Woosters, when Aunt Dahlia offers to sacrifice her cook Anatole to save Bertie from thirty days in the clink. Also subsequently, when Bertie turns her down.
A subtle one at the end of the fourth episode of the second season: Jeeves comments that he has returned to Bertie due to both Chuffy and Mr Stoker failing to meet the requirements for him to be employed by them - with the implication that Bertie does meet his high standards.
Bertie, quoting Alexander Pope, referring to Jeeves as his "guide, philosopher, and friend.''
Another subtle one: In Much Obliged, Jeeves, when Mrs McCorkadale comes to call on Aunt Dahlia and tells her that she has "just had a visit from a slimy, stinking slug." Bertie, who has visited her the same day (he was going around to tell people to vote for his friend Ginger in the upcoming local election, unaware that Mrs McCorkadale was Ginger's opponent in the same election), thinks that she's talking about him and that this was unnecessarily harsh of her — and Aunt Dahlia makes the same assumption, as she says in an ice-cold voice: "Are you referring to my nephew Bertram Wooster?!" It's a small moment, but Aunt Dahlia's instant indignation when she thinks Bertie is being slandered really shows her devotion to him — she's the first to hurl good-natured insults at her nephew and doesn't even mind if people question his intelligence, but she absolutely will not tolerate anyone questioning his moral character.