The Sunday New York Times had an interesting Magazine article titled "In Pursuit of the Perfect Brainstorm" by David Segal. The article documented a company that employs a variety of ideation and management techniques to generate new ideas for businesses.
Here is the URL. You might need a Times account to access.
The company helps other companies come up with "ideas to solve what it calls 'highly ambiguous problems." One example from the article was a request from the candymaker, Mars, to define the current meaning of "indulgence".
Some points from the article:
1. Traditional brainstorming can easily devolve into a competitive game with a vague unstated goal of "winning" - that is bad.
2. The "yes and...." approach is used to move from traditional brainstorming to storytelling. In the "Yes and" approach, a person offers the first sentence of a story and then someone says, "yes, and..." and someone else fills in another line of the story. The claim is that this is more collaborative than group brainstorming. One could argue that there is still friendly competition in this storytelling method.
3. Reverse brainstorming. In the article, the topic was "to come up with an idea that would make air travel seem completely unbearable.". Reverse brainstorming is a method that can be used when a group is struggling for positive ideas - brainstorm bad ideas and then switch and see how you can solve the bad ideas.
4. The 30-30 rule - "30 percent of the people who make strategic decisions should be 30 years old or younger". This is part of the 3-box framework where Box 1 is what a company does not to manage and improve performance; Box 2 is "selectively forgetting the past" where you dispense with traditional rivalries and dated trends; Box 3 is future strategic thinking.
5. Many breakthroughs occur at times of reflection - the "great idea in the shower" phenomenon.
6. Shopping for metaphors is a method where you send teams to different types of stores and ask them to "buy something that is a metaphor for the solution'". This is like metaphor brainstorming.
An interesting article in that it described 5-6 non-traditional techniques for generating ideas and gave examples of what people came up with based on those techniques.