For instance, if I am working on a book chapter or an article, or if I need a new solution for a client's business problem, I put that into my mental hopper and let it sit. We've mentioned a number already. One way to stimulate unconscious thinking is to engage in physical exercise. The key is they are all sort of mindless - not requiring much detailed thought. Likewise, playing a rhythm instrument like drums or bass, or any sort of rhythmic chanting or dancing, will produce a similar result.
Mind mapping is an excellent technique for tapping the unconscious.
Drawing representations of your problems and possible solutions, however crudely, also works well. For truly graphically challenged, try collages made from cutout images. Sometimes just flipping though magazines will stimulate ideas. There are activities which you can do in groups. You can play word association games.