The Storymatic includes two sets of cards that when put together randomly sparks potential stories and ideas. You could also collect your own and start your own deck of cards to build ideas.
Rory’s Story Cubes comes in various types from adult to even children’s versions. The concept is similar, except the dice rolled include pictures. You can lay them out in a plot, or use the cubes as the elements of a story such as characters, theme, conflict, and so forth.
The Amazing Story Generator is not so much a game but does something similar as the story cubes. Instead of pictures or cubes, you get a flip book broken up into three sections to randomly pick elements of a story.
You could also use the card game Munchkin to provoke ideas for storytelling, in particular, fantasy, role playing type stories. Draw cards to add characters or story elements.
Iphone, Android, and tablet apps also offer some fun prompts. I use Writing Prompts for the Iphone to randomly view prompts, scenes, even pictures. You can then save to favorites. You can also add your own prompts as inspiration hits you.