In the first game, after the first boss is defeated, he tells Richard that Rachel was taken to the watchtower. He adds, "She must be dead by now." Not a second after he finishes saying this, Richard clocks him in the face and runs off.
In 3, the game starts off with Alan and Wesley in their vacation disguise until the Zagorian soldiers arrive and one of them says, "What do you think you're doing here? This is a restricted area!" Alan and Wesley then run inside the boat, and the soldiers follow them. Once inside, a bomb is slowly counting to zero, which then says "BYE!" as it explodes. One of the soldiers says, "Oh my g..." before the boat explodes and Alan and Wesley take off in their own boats.
Also from 3:
Wesley: "Are you sure we're heading right way?"
Alan: "Actually, I was just following you..."
Alan: "Well, guess we came to the right place.
A lot of the banter between Captain Rush and Mathers in the fourth game, especially since he's the only boss who gives dialogue in the series as well as Beth commenting on the fight, with her saying, "F...!"
Note that she doesn't pronounce it like "Fuh"; she actually says the letter "F".
The "stage cleared" screen is accompanied by a boxing knock-ou bell.
Also in 4, this exchange between Giorgio and Evan: