SpaceJump is an old theatre warmup game I used to play back in uni.  It's probably stolen from Whose Line Is It Anyway (though this time, I didn't steal it.)

The original game

In theatre, the game needs a group of at least five or six people. The game starts with three people - the Performers -  "on the stage" who improvise a small scene. There's no planning beforehand, and no props; one person starts making something up, and the others follow along.

The rest of the group - the Audience - watch. Each of them can yell 'SpaceJump' whenever they want. Whenever someone yells 'Spacejump', the three Performers freeze in their current action, no matter what they're doing. Whoever yelled 'SpaceJump' runs in, taps one of the Performers on the shoulder and replaces them. The ex-Performer returns to the Audience, and the new Performer holds the exact position until the group unfreezes. The new Performer then takes the improvised skit in a completely new direction.

For example, the initial improvisation may have been a dinner scene between two people, with a waiter leaning down to serve one of them. Someone yells SpaceJump, replaces the waiter, and turns the scene into an interrogation scene. As the waiter/interrogator turns to fetch the hot pokers, someone yells Spacejump, replaces one of the interrogatees, and turns the scene into a hypnotist's performance. And so on.

As a writing game

You'll need at least two people, five or six is better. Agree on the location of the scene, eg "a french restaurant". Everyone starts making up whatever is happening in that french restaurant.

At some point, when they feel like it, one  of the group yells 'Space Jump" (anyone can call it at any time). Everyone:

1. stops writing, even if it's mid-word,  
2. folds down their paper so only the last three to five sentences are visible
3. passes their story to the left.
4. The person who called 'Spacejump' announces a new thing that will be introduced into the story, for example "A man with a gun". (Note: they don't say what he does. Just that he's there.)
5. Each person then reads the last three-to-five sentences they just received and continues the story, including the 'thing' that's just been announced.
6. Repeat when someone else yells 'SpaceJump'.

The reason you're limited to five sentences is to stop the game being bogged down with people reading what happened before, or trying to think of "something good". If you don't have the whole context, you're freed from the obligation to make sure what you're writing fits what happened before.

Alternatives

A simpler version that doesn't involve story-swapping: whenever someone yells 'SpaceJump', they announce their one thing. This gets written in to everyone's story, wherever they are. The SpaceJumper can also elect to remove one thing (say, the man in the gun goes away). If you're playing it this way, it's a good idea to have someone keeping track of what's been introduced on a whiteboard.