The Imperial commander's lines in II's Capture The Flag mode. Hearing him say "The Rebels have foolishly dropped the flag," conjures up an image of a Rebel carrying the flag along and then just kind of spontaneously deciding to throw it away because he forgot what he was supposed to do with it or something. "Whoever dropped the flag will pay for their incompetence!" is also a good one.
One of the built-in cheat codes is for "Party Effects Mode". These effects include comic-book style hit effects when someone gets smacked with a lightsaber, and humorous captions when Rebels are killed by Wampas.
On maps in II where the CIS' "hero" unit is Jango Fett, troopers will occasionally remark "It's Jango! And he brought his head!"
In both games, the Rebel Alliance has different tank unit. Both, however, have the exact same backstory of designs lost by engineers from the same company in a game of Sabacc and picked up by the Alliance. Both designs are considered canon (for the old EU, anyway), as they have both appeared in other games, meaning either both designs were lost at the same time, or the same incident happened to the same company on two separate occasions.
The very few ways you can kill Hero units in SWBF 1 are amusing in context. The idea of Darth Vader, the highly-feared Supreme Commander of the Galactic Empire, getting killed because a rebel on a speeder bike rammed into him can be pretty damn funny.