The budding friendship between Richard and Long John Silver, with Richard pretty much taking Jim Hawkins's place in the story, it was bound to happen.
Richard's friendship with all the books is a good example.
The scene near the end when the Pagemaster summoned the four characters Richard had to face in his challenges. They all congratulate him, each in their own way.
Jekyll: You prevailed over evil.
Ahab: Ah, you looked Moby Dick in the eye, boy.
Silver: Y'got the pirate stuff, m'lad. And don't let no one tell ya diff'rent.
Dragon: (folds its wings majestically, as if in a salute) SKREEEEEEEEEEE!
The very end of the film, when Richard's parents find him asleep in the treehouse, finally having gotten over his fear of climbing the tree.
And almost immediately prior to that, when Richard sees the ramp the other kids were jumping. He stares at it a moment, licks his lips... and pedals top-speed at it, and jumps it, letting out a triumphant "YES!" as he lands. It's even better in the novelization, when the kids from before are watching.
At the end, Richard, who told all three books that he'd check them out, is told he can only take two. The librarian, Mr. Dewey, removes Horror from the top of the stack. Richard protests.
"But I promised I'd check him out.
"You promised whom?"
Richard pointed to Horror. "Him...I mean...umm... Do you think just this once I could?... Please, Mr. Dewey, I really need..."