Prince Kabala of Kapetapek teaching Racer X how to drive on dangerous mountain roads. Racer X himself states that Kabala was kind and helpful to him, and in turn, Racer X repaid his kindness by impersonating as him to keep the borders of Kapetapek safe.
Pops telling Speed that he can come home anytime, despite Pops disagreeing with why he's leaving. This borders on Tear Jerker territory when you remember that the last thing Pops told Rex was that if he left, he was no longer welcome in the Racer home. You can tell Pops was adament not to repeat past mistakes, and it shows.
Racer X anytime he compliments Speed, especially the montage at the end that reveals his Secret Identity as the long-thought-dead Rex Racer.
Sparky and Speed having their last conversation before the last race.
Sparky: [I] just wanted to say thanks, for what could be the most exciting moment of my life.
Speed: Couldn't have gotten here without you.
Sparky: I'm looking forward to that cold milk.
Speed: Me, too.
Note how they're not even questioning whether or not they will win, but are instead anticipating sharing the moment together, as a family. And for all intents and purposes Sparky is a member of the family.
The very first race shows Speed racing against the memory of his brother, who set the fastest ever time on that course. As he approaches the finish line, you see the two neck-and-neck until Speed eases off the gas, allowing Rex's record to stand.
When Taejo's sister makes up for his double-crossing of Speed and the C.I.B. and uses Loophole Abuse to help Speed enter the Grand Prix. To his credit, his smile when Speed arrives shows that he has no problem with what she did and cheers Speed on throughout the race.
Speed and Trixie hitting it off immediately as children, after Trixie punches another girl out for making fun of him.
Really, every scene shared by Speed and Trixie is just dripping with "dawwwwwww".