Disclaimer: This is a bit of a religious issue with Quake addicts and overclockers, and the cause of many a holy war (try typing "60 fps" into Google). Everybody is different, and your eyes may be more sensitive to low fps than others'. YMMV. Feel free to substitute your favorite FPS for each instance of the word Quake.
Conventional cinemas project 35mm film at 24 unique frames per second. Each frame, however, is displayed 2-3 times1, for a scan rate of 48-72 Hz. Persistence of vision lasts for around a 50th of a second, so a source must strobe at at least 50Hz to appear as a solid image. To give a convincing illusion of movement, 20 fps is about the lower limit - below this the film will look like a series of images. The debatable bit is whether the brain can tell the difference between 25 and 50 (or more) unique frames per second. Quake players claim they can tell, especially when the POV is panning rapidly. Each frame of a pan in quake is a perfectly clear snapshot of the view from the current direction, with no blurring, and therefore no motion cues. When a film camera2 (or indeed an eye) pans, each frame is a composite image of everything the camera 'saw' in the exposure time of the film, potentially a lot more information. 24 fps may, therefore, be much more acceptable in a film than a computer game.
IMAX film is projected at 48fps, and is generally seen as more convincing than regular cinema at portraying very fast motion. Of course, the screen being three stories high probably helps too... But how many real films have first person bobsled scenes in them? Why go to the expense for something producers are unlikely to make use of, and the audience may or may not be able to perceive? The stakes are higher, of course, in quake - if you can't see what's going on, or get confused momentarily, you'll get shot. Feeding as much information to the player as possible is definitely worth it.
Personally, I believe I can tell the difference between 40 and 60 fps in a game, but I've never noticed movies going 'choppy'... IMAX screens (and the back to the future ride) do look noticeably nicer than regular cinema, though.
1 - In a film projector, this is done by the secondary shutter, which rotates at the same rate as the primary shutter, but has 2 or more times the teeth. The primary shutter hides the advancing film, while the secondary shutter strobes the lamp. TVs show the same frame more than once too - they project the odd and even rows of each frame in two different passes, so that the picture strobes at 50/59.94 Hz, despite being only 25/29.97 fps. (see interlacing, cinecompression)
2 - I'm not sure what digital movie cameras (Star Wars: Episode I - The Phantom Menace, for example, was filmed, post-produced, and (in some cinemas) projected digitally) do in this situation though...
Cheers to riverrun for putting me right on framerates!