Made famous by Whose Line Is It Anyway? and the short lived Kwik Wits on television and by Comedy Sportz theatres across the country, short form improv is more a series of games than a series of scenes. It is also sometimes referred to as cabaret style improv because of its intimate nature with the audience. Players are given quick suggestions from a host or sometimes the audience and begin, depending highly on one liners, wit and puns rather than on development of character, exposition or scene painting, which is crucial to long form improv, which can develop into sketch comedy like we see on Mad TV and Saturday Night Live.
Some of the more famous short form games are (and they often go by different names):
Freeze Tag - Short scenes where other players call out for the scene to freeze and then take over one of the players, completely changing the scene
Novelists - where each player takes on the persona of a famous author and then the group tells a story, each taking a portion and interpreting in the style of Dr. Seuss or Charles Dickens or Eric Bogosian or whatever.
One line answer games like World's Worst - Players are lined up and presented with a category like
"Things You Don't Want to Hear On A First Date" and must fire off quick, one line answers in succession.
Short form improv is often set up as a competition of sorts, with players being divided into teams and earning points to "win" the evening.