Here are some examples of interesting "quick cuts" I've come across recently.
Mean Streets (1973)
The entire title sequence is incredible---from the cut to a projector that comes out of nowhere, to the home movie, to the music---but the cutting that takes place in between the shots of Charlie's head hitting the pillow is what I want to talk about. As the character falls back in slow-motion, the camera cuts closer and closer to his face. Yes, the editing matches the beat of the music, but abrupt cutting of a single action paired with the slow-motion is fascinating. It is at once both jarring and dream-like, informing us that we are about the enter Charlie's psyche, one of heavy conflict, contradictions, and sensual rawness.
Stolen Kisses (1968)
(Note: Obviously, we'd get a better sense of the rhythm editing with a video, but I couldn't find a clip of this scene anywhere.)
Working as a detective, Antoine Doinel loses sight of the magician he's suppose to be tailing when he decides make a phone call to his girlfriend. Realizing this, he exits the phone booth in a hurry. In what could have been filmed within one shot, what we get instead is an odd series of shots from two different perspectives of him leaving: One from an interior shot in the booth and one exterior. The sort of "rack" cutting of between the two shots happen rapidly, lasting less than a second. It's almost like a subliminal message or even a glitch, as if someone accidentally included a couple frames from the next shot when cutting the scene together. This disruption in the follow of Antoine's exit heightens the anxiety of the situation (though rather quickly) with the flash of the interior shot attempting the keep Antoine within the booth when he clearly needs to leave.
Let me stress the fact that the cuts are telling us this information, not necessarily what is happening within the shot.
The Color Wheel (2011)
This example is a little different of the first two. It's more about condensing time and space than adding extra information to the scene.
At first glance, the cutting of this transition moment between locations seems somewhat strange. As the brother and sister duo, Colin and JR, make their way from a motel to the diner, we first see a shot of a car driving on the road, then a cut to the car pulling up to the diner, and a final cut of the car already parked with Colin and JR walking into the restaurant. We have witnessed a jump-cut people! What make this interesting is that the attempt to condense time is somewhat negated by the car moving in the first two shots and then is stationary in the last one.
It's weird.