I realized something peculiar over the years, I cannot think deeply while sitting on my desk! Whenever I try to solve a hard problem, design some parts of a program, and generally do anything that requires more than two minutes of pure thinking, I get off my desk and start walking.
Whether I pace up and down the hallway, walk in circles around a table, or just have a small walk outside, I find that my thoughts become much clearer. I come up with my best ideas while walking, and I can solve the hardest problems much faster. Of course, people who see me doing it indoors usually give me a weird look and think I'm insane, but it doesn't matter, I'm more productive this way!
I've seen people do other things to help them think, such as tap a pencil on the desk, squeeze a stress ball, or throw their heads backwards and stare at the ceiling. I am interested in what you people do to trigger your thought process.