I want to distinguish toys from three other IF game elements: Puzzles require the player to find a solution to a problem in the narrative. If she can't find a solution, she's stuck. Branching allows the player to steer the plot of the narrative. Role-play allows the player to control character traits/abilities of the narrative's player character.
Toys, the focus of this poll, allow the player to, well... 'toy,' or generally monkey around, with a particular element of the game without punishments or decisive effects. I submit Lost Pig by Admiral Jota, Metamorphoses by Emily Short, and The Island of Doctor Wooby by Ryan Veeder as prime examples of games with toys. All three works include freely manipulable props. Lost Pig also includes a well-implemented and forgiving conversational NPC.
So what other toys have you enjoyed experimenting with? Please include the in-game name and in-game location of the toy in your comments.