How many times have you come out of a brainstorming session feeling unsatisfied with the results? The team never felt like it got into a rhythm. The idea flow felt like a drizzle versus a storm. None of the ideas that the team spent much time on seemed especially good (BTW, you should never spend a lot of time on any one idea in a brainstorming session). There was one or two people that insisted on dominating the conversation and ended up speaking way too much. This to the frustration of the rest of the group. The good news is that there are just a handful of things you need to do to run a productive and fun brainstorming session.
The overall goal of any brainstorming is to generate a high quantity of ideas. This is really important ... it's all about quantity, NOT quality. You will have plenty of opportunity after brainstorming to evaluate the quality of the ideas generated and select a winner.