I, myself, don't participate. But I have far too many friends who do (including my wife). And, over the years, I've accumulated a number of games which can help sharpen that storytelling edge.
Those of who who are NaNoing should look into some or all of the below:
Dixit (and/or any of its expansions): If you're not going to be actually playing it as a game, then don't worry about whether an expansion is standalone or not. If you're writing any sort of fantasy, then use the images as inspiration. Use them for character backgrounds or plot points or however you want.
Rory's Story Cubes: There are three sets available in North America. If you're in Europe, there are three (smaller) sets available as well. If you get stuck for an idea, roll the dice and see if they help. The base set is mostly things, the expansions include one set of actions and one set of voyages. Each of these sets is nine dice with images instead of numbers. Roll and then pick-and-choose. The three European-only (so far) sets are Clues, Enchanted, and Prehistoria. Each of these sets contains only three dice.
Short Order Heroes: Having trouble coming up with personalities for those minor supporting characters who pop up occasionally? Maybe it's a "one-time" character that you'll never see again. Flip a couple of cards from this game up, and you have those character traits covered.
Texas Zombies: This is a deck of things. It was designed as a storytelling game where you used the things in the deck to overcome obstacles within the deck. You can play it to sharpen your storytelling edge, or you can use the cards to see what sort of inspiration appears.
Story War: This is in a similar vein to Texas Zombies, but has different kinds of cards - the base set includes 50 Warriors, 25 Items, and 25 Battlefields. You can - again - play the game to sharpen your storytelling edge or you can mine the decks for ideas.