The moment on the Death Road in Bolivia between May and Hammond when all May could see in the dark was the back of Hammond's Toyota.
May: Hammond, I want to say something to you that I wouldn't say at any other time. Hammond: What? May: Please don't leave me. Hammond: Oh God, those words are going to stay with me for a bit, I'll struggle to get over that. [more sincerely] No, I won't.
Just a small thing, but in the episode in which Hammond is hypnotized by Paul Mckenna in the studio, to check that he truly has been 'put to sleep', so to speak, Clarkson leans forward and says the following:
It just seems so sweet that Clarkson knows him well enough to know that if he were awake, he would respond to him.
It's more of a Crowning Moment of Cute, really, but during the Race to the London Airport challenge, The Stig is waiting at a bus stop when he's accosted by a flock of children. They're still in class, so they have to leave, and they all wish The Stig the best on his race.
Little happy child: Good luck on the bus!
Hammond taking a picture for the children in the village between Hanoi and Ha Long. Sweeeeet!
When trekking through the Himalayas in the India special, the gang is forced to camp in freezing weather due to Hammond's failing lights. While no one is happy about this, what follows is a genuinely tender moment between mates without all the vitriol that usually divides them.
In the same special, Hammond got one of the Mini's headlights to work at the very end. It was a real scrapper.