As I'm thinking of it now, the Official White House Briefing Drinking Game will have two parts: A Master List, covering all briefings, and a Daily Addendum, which would correspond to that day's briefing. Here are some thoughts about what might be included in the Master List. Please email or add comments with further suggestions:
Dog/puppy
Critical investments
Jobs
"I read in the paper"/"your paper"
Sports metaphors
Gibbs takes a drink of water
Helen asks about war crimes
Doogie Howser asks a question
Science fiction reference
Simpsons reference
"Study after study"
"The Gibbsie" (Towards the end of the briefing delivering a clearly rehearsed mini monologue on a topic that is only vaguely related to the question asked)
pre-judge
"don't want to get ahead"
"I haven't discussed [INSERT THE MOST PRESSING ISSUE OF THE DAY] with [person in charge of it] yet"