Robert mentions the book on Villains by Thomas and Johnston (and their 'Illusion of LIfe' of course is well known to animators) but their other book 'Too Funny For Words: Disney's Greatest Sight Gags' provides good insight into how to 'write' animated sequences without words.
The concept of 'the gag' has largely fallen out of favor but the underlying idea of entertainment and humor is still just as popular.
Something I find interesting is how Disney got the entire staff involved in coming up with good storytelling visuals and some even made some extra income by submitting gags that were used in their films. I'm sure it led to more than a few promotions as well.
In part 2 Frank and Ollie break gags down into the following basic categories.
The Spot Gag
The Running Gag
The Gag-That-Builds
The Action Gag
The Tableau Gag
The Inanimate Character Gag
The Funny Drawing
Specialized Gags (Color, Effects and Caricature)
It is also very interesting to me how this approach to 'writing' pulls in aspects of thumbnailing, brainstorming, storyboards, etc.
The whole idea being that while dialogue and other elements of story are important it is essential to tell the story through visuals; pantomime, character, performance, mood, etc. to the point where the story can be told without them but then is plussed up even more through their inclusion.
The Disney approach was of course heavily influenced by silent film and that carries through well into caricatured performances.
Most of the illustrations in the book have been posted online in some form or fashion over the years but the book is unique in it's collecting of the story gags into general categories. This not to present a formulaic approach so much as to explore what makes visual storytelling work. This thought and theory then can be applied to the creation of shorts and films in animation or live action.
Note: There are several books with the title 'Too Funny for Words' out there so if purchasing online make sure it's the right one.