Plenty of these in the series, but PJ confessing his love to Rose and Max choosing to face a blizzard to find Goofy during the Christmas episode are some of the most memorable ones.
The chestnut speech in "O, R-V, I N-V U". Especially if you identify with PJ. And if you keep in mind that Goofy is effectively serving as a Parental Substitute for PJ's own (inadequate) father. What really makes the scene is how profoundly the speech affected PJ, who changed from dismissing the chestnuts to gathering them in large quantities, which even turned out to be a Chekhov's Gun. Then when he does "come out of his shell" in the second movie... it becomes Heartwarming In Hindsight too.
Goofy: Is there something wrong?
PJ(plaintively): Do I look dumb to you?
Goofy: No way, PJ! Here's dumb! (tosses chestnut at PJ's head)
PJ: Ow! (looks at nut) What's this?
Goofy: A chestnut.
Goofy: Not too perty on the outside, huh? It's all spiny and dull-looking.
Goofy: (takes chestnut from PJ and begins shelling it) But come the right time, the shell falls off and walla! Look at it! Ah-hyuck! (inner nut is shown) It's chock-full of good stuff, (cuddles PJ) and handsome too. Ah-hyuck! (touches PJ's nose affectionately) You know what I mean?
PJ(smiling softly): Yeah, I think I do...
Max coming up with two very elaborate plans to make it so that PJ could be friends with him in "Good Neighbor Goof" (the second half of the pilot), after PJ had been abused in Max's earshot, had been forbidden from seeing him, had revealed that Max was a Living Emotional Crutch, and had given up. It really seems to excuse any moment Max seems to take PJ for granted, and completely justifies PJ's fervently loyal behavior to Max in later episodes.
Max (and Peg) defending Goofy from Mrs. Pennypacker in "Date with Destiny", and then her taking back her judgment when Goofy rushes over to comfort Max after his nightmare.
Goofy and Max winning the best father and son pair in the class in "Meanwhile, Back at the Ramp" because they'd do anything for each other.
Even Pete of all people gets a few, like the time he gave a Participation Trophy to the kid at the end of "Tee for Two".