In a bit of a twisted way, Riddler and Two Face's Villainous Friendship. The two never turn on each other, barely bicker at all after joining up, and seem to be having the time of their lives whenever they're on screen together. It's not often you see live action villain not only work together successfully, but get along like best buds.
Chase admitting to Batman that she's gotten over her childish crush and has feelings for another. Bruce feigns disappointment as The Bat, but smiles to himself (and the camera) once he turns away.
Before Two-Face's death, the way he calls Bruce a friend before flipping his coin almost sounded like his humanity surfacing one final time.
Batman: Aren't you forgetting something Harvey? Your coin. You were always two minds about everything.
Two-Face: Yes, of course, you're right Bruce. Emotions always the enemy of true justice. Thank you. You've always been a good friend.
Although it's presented much less effectively across the Burton and Schumacher films as it is in the newer Nolan films, the relationship between Batman and Commissioner Gordon is at its very best across the four films here; Batman blasting through the Riddler's projection over the Batsignal and giving Gordon a thumbs up to let him know everything will be okay, and Gordon cheering him on as he heads for the final showdown. It's a really brief but awesome payoff to the "He gave us the signal!" moment in Batman '89.
The Deleted Scene in The Bat Cave with Bruce Finding his father's journal and discovering that he wasnt responsible for his parents death.