Over on the Ideo Blog, there's a great post on brainstorming methods that work particularly well for introverts. Lots of good ideas here, and you should incorporate at least one of these methods every time you brainstorm because there are always introverts in your group. Here are our two favorites:
The Silent Circuit: Ask each person to write a “how might we” question on a sticky note (IDEO’s standard brainstorm kickoff question) and post it around the room. For about 15 minutes, everyone walks around, silently adding as many ideas as they can to each prompt. When time’s up, everyone returns to their question and discovers a bounty of new ideas that their colleagues have given them. This approach works well for keeping large groups engaged, while providing quiet, focused time to those who want it.
Musical Chairs: Breaking up a big group helps encourage quieter voices. To limit the number of people in a brainstorm, split into groups of three or four and play musical chairs. Post a handful of "how might we" questions around the room, assign a group to each one, and start the music. When it stops, rotate to the next station with your team. That way, there are never too many voices to contend with, but a lot of ideas are shared. Leave time at the end for people to wander around the room and add any remaining ideas.