Agent J's got a couple, mostly for the quotes given by Will Smith afterward:
Before he joins the MIB, he chases after an alien on foot and tackles him to the ground, while saying:
J: "You see this [badge]?! Huh?! N! Y! P! D! Means I will kNock Your Punk-ass Down!" Alien!Perp: (out of breath, panting) He's coming... he's coming... J: Yeah, and when he gets here, I'll arrest his ass too!
J being able to chase the alien down on foot — an alien capable of running up walls — was what convinced K that he would make a good replacement.
During the MIB session at the shooting range, there's J's rebuttal in defense of him shooting an eight-year-old girl instead of the "obviously" vicious-looking aliens. His explanation? The aliens were simply minding their own business, but there was Tiffany, a little white girl in the middle of the ghetto in the middle of night, carrying a handful of quantum physics textbooks way too advanced for a kid her age, so she had to be starting something.
The animated series reveals that the little girl guise is the preferred disguise of the Bug Queen. The little girl really is the most dangerous thing in that alley.
In the novelization dialogue between K and Z reveals that J actually did pick the right target. The "monsters" were depictions of ugly but totally harmless alien species!
"Or do I owe her an apology?"
Enjoy your new threads, Mr. Smith. You won't need any others.
After he dons his MIB gear for the first time:
"You know the difference between you and me? I make this look good."
It also should be noted that J obviously wants to move out of the way of the crashing spaceship, but holds his ground because K just isn't fazed.
The Reveal at the end of the film (even if it was Jossed at the end of the second) that the entire Milky Way galaxy was, just like The Galaxy, a marble. In this case, one of many in an alien's collection.
Men in Black II
Kay, with on the fly instructions from Jay after getting his memory back, singlehandedly beating down a room full of alien thugs.
Men in Black III
Boris the Animal's escape from Lunar Max prison at the start of the film, all of it, but particularly "It's a bit stuffy in here. I think I'llopen a window."
J's father near the end of the film, talking about how important both of the Agents were to the future, and selflessly aiding them. Goes into Fridge Brilliance when you realize that he probably knew his actions would result in his own death, but that he doesn't care since his son's life is on the line, thanks to being shown the future.
Let's face it, time-traveling by jumping off of the freaking Chrysler Building takes some serious balls.
Griffin's ability to see all possible timelines is awesome in and of itself.