When I started my first (and last) official project management position someone gave me some useful advice, which I pass on here. Project politics is very important and you have two choices
  1. If you are good at politics you can play the game, and if you are really good, that will make you a better project manager
  2. If you are not so good at the politics then ignore them. Just do your job -- manage budget, schedule, scope and risk. Show that you are not doing the politics crap and you can get away with it.
This seemed very odd advice at the time, but as I am not a great politician I followed the second option and it has always served me well -- even if it has caused a few surprises to my customers and colleagues over the years. Updated 1/Dec/06 Obvioulsy this is a rather simplistic stricture, how can you possibly ignore the politics? Well in truth of course you should'nt -- as far as possible you must take note of people; what they are saying (compared to what they are doing) and how they relate to others. This will give you valuable information in identifiying possible issues and risks. However you need to offer no political opinions, show no preferences and make sure that everyone sees your decision process is fair and fact based. What you say and what you do should have nothing to do with politics.