In "A Zeo Beginning, Part 1": "Hello Rangers, welcome home."
In "A Zeo Beginning, Part 2", Zordon officially gives the Rangers their new powers. When he gets to Rocky and says that he is now Zeo Ranger 3... Blue... the camera cuts to Billy (who had just given up his spot as a Ranger) and he sighs... and Alpha 5 puts a hand on his shoulder. Even though it was Billy's idea, that moment showed that the finality of his decision wasn't lost on him. For the viewers, that and the later shot of the old Mighty Morphin uniforms in display cases showed that it really was the end of an era, as Billy was the last of the original five.
Similar to Billy, when the Zeo Crystal first fragments and gives the Rangers their new powers and colors, Rocky looks around for the red crystal the moment he realizes he's going from Red Ranger to Blue Ranger.
Similarly, when Zordon tells Adam he is now the Green Ranger, Tommy briefly turns his head to him. Even though he lost his Green Ranger powers long ago, and spent several recent months as the White Ranger, he too feels how Rocky and Billy feel.
Also, the look on Tanya's face when Billy tells her that she's now a Ranger.
Really, it's the whole sequence of the Rangers receiving the Zeo powers, with how Zordon speaks to them like a father on his children's graduation day, which, in essence, this is for them, graduating from the Mighty Morphin Power Rangers to the Power Rangers Zeo.
In "Shooting Star," when Tanya comes to the other Rangers with a problem, Adam assures her that the Rangers are her friends and will help her.
There's an episode whereupon we learn that Skull is actually a damn good piano player. However, he keeps it a secret because Bulk is always making fun of classical music and people who play it. The end of the episode has him performing, and, instead of laughing, Bulk is genuinely moved by his pal's piano skills. It's not everyday on this show that we see a heartwarming ending from the comic relief duo, but yeah, we definitely got it here.
In "A Golden Homecoming," Jason returns to claim the Gold Ranger powers. As he and Tommy practice at the end of the episode:
Jason: Leaving was a really tough decision for me, but I'll tell you what it made it cool. I knew I was leavin' the Rangers in good hands; I mean with you as their leader.
Jason: But I don't want you to think that I'm tryin' to like put things back to the way they were before I left.
Tommy: Listen, I mean, the Power Rangers are a team. No one's more or less important than anyone else.
Jason: You're right, man. It's good to be back, Bro.
Before Jason comes in as the Gold Ranger, the Rangers are told they need to find someone to take the power. With absolutely zero hesitation, they send Trey to Billy, who willingly surrendered his powers to Rocky when there could only be 5 Zeo Rangers.
When in "King for a Day" Kat gives Tommy a hug (while de-morphed) in order to snap him out of his Brainwashed and Crazy state despite the risks, and it works!
The end of "Rangers of Two Worlds, Part Two" has Billy deciding to stay in Aquitar to get long-term treatment for his rapid aging issues. The episode itself ends with a montage of Billy's best moments from the past four seasons in lieu of the usual blooper reel, and is a perfect farewell for the longest-tenured of the original five Rangers.