In the third part of "The Ultimate Doom", Sparkplug thanks Spike and the Autobots for coming back to Cybertron to save him from the Decepticons after getting brainwashed, to which Spike replies "It's like you taught me, Dad: You never quit on the people you love."
Brawn lampshades this by retorting "Mushy, but true..."
When Grimlock reconciles with Optimus Prime and shakes his hand in friendship for the very first time:
"Me Grimlock was jealous of Optimus Prime."
The last 30 seconds of "The Return of Optimus Prime Part 1" is the Heartwarming Moment of Transformers.
Sky Lynx: Our leader is back.
Optimus: Yes, Sky Lynx, and this time, no force in the universe can stop me.
It's takes about two seconds before Cyclonus is convinced it's time to act.
Cyclonus: No, release him! Let him go!
To put it into context with his loyalty, throughout the episode his main concern was Galvatron and openly questioned the Doctor's orders and while going through the ream of paperwork he looked back at the cage carrying his unconscious leader away. He was willing to risk his life if it meant Galvatron could be cured of his insanity and after the Ayla Solution backfired (as mentioned before he tried to save Galvatron from the lobotomy) he stayed by Galvatron's side and admitted it was his fault (he got hit for his troubles) and followed Galvatron into the crevisse where he destroyed the Memory Core. That is loyalty.
Cyclonus was the only Decepticon not to leave Galvatron's side in 'The Burden Hardest to Bear'
Hoist and Grapple in the episode "the Master Builders" manage to show a deep friendship in the span of only thirty minutes, especially the last lines of the episode.
Hoist: There'll be other towers to design and build, Grapple.
Grapple: It was magnificent, for a little while. Wasn't it, Hoist?
Any time Bumblebee gets a little recognition. He's always so grateful, but in a humble way.
In "Dinobot Island", Bumblebee wraps up a call with Optimus Prime and gleefully remarks to himself, "I didn't know (Optimus) thought so much of me!"
It's not really touched upon in the cartoon, but in almost all G1 continuities, Bumblebee feels insecure about his size, and is always trying to impress the Autobots he looks up to. What he doesn't realize is that because of his endless determination they look up to him.
A lot of the interaction between Daniel and Arcee. Her motherly nature towards the boy can be the source of many a Warm And Fuzzy Feeling.
When Skyfire is found frozen in the Arctic in "Fire in the Sky" by the Decepticons, they take him back and thaw him out at thier base. Starscream takes over the efforts to reactivate him and acts very concerned, explaining that he was a friend of his before the war began. Now Skyfire, being naive about the war and rather big and powerful, would be a valuable ally against Megatron, and it could be argued that this was Starscream's motivation. However, not only did he show no signs of an ulterior motive, he sounded genuinely concerned, and didn't bother trying to mask it with arrogance or bravado. This troper can't recall offhand a time Starscream ever demonstrated real concern for anyone but himself before or after this episode, so this moment in particular was very touching.
While it's mostly do to the limited 80's writing, it's was great to see that Hot Rod held no grudge against Optimus Prime being made leader of the Autobots again after he gets the Matrix back in "The Return of Optimus Prime". Hot Rod doesn't care about losing his role as leader, he's just glad to have Optimus back.