I like to use the rubberducking technique:
Place a rubber duck on your monitor and describe your problems to it. There's something magical about stating your problems aloud that makes the solution more clear.
(See also Rubberducking and creativity.)
I'm also experimenting with defining my 'audience' during rubberducking: I create a list of people and choose one to be my audience. I imagine how I would explain the problem to that person. I ensure I create a multifarious list that includes children ('how would you explain your problem to a child?' is good advice), the great and the good, and even eccentric people.
Thinking during brainstorms
Since 1994 I've always scribbled on paper as I brainstorm. As a result I've come to find it difficult to think without pen and paper in front of me! I've experimented with ways to think without paper: thinking to songs is one approach I enjoy. Recently I've been using an approach where I select a person from a list and imagine that the person is in the same room talking to me about a problem I'm working on (or a creative focus). I make an effort to mentally hear their voice.