“The Game” too often has suck-up and backstabby connotations. I’d like to spin elements in a more positive light, you can be a game player without trampling your peers. Yes, you do have to put on an actor’s face, but you don’t have to bring it home with you.
– Deliver a product (widget, speech, service etc) that they want, not what you want them to want. No matter how valuable your 1000 hrs of toil, labor, and analysis is, if at the end of the day your boss wants a single bar chart and a thumbs up and your 100 page dissertation goes in the recycling, then just smile and don’t whine about how hard it was.
– Always give at least a token ear or effort to anything anyone has to say. That whiny shrew in finance auditing can either whine positively or negatively to others about you.
–Be positive, but don’t be the annoying perky cheerleader or morale booster. Bringing in a box of occaisonal donuts will win you far more points than being labeled “United Way guy”.
–Keep a work/life separation, don’t get drunk with the boss. The friends you make outside of work are better and won’t hurt your career if they turn sour.
–Always compliment your peers for what they did, even if you couldn’t care less. Popping into a cubicle and saying “Great presentation, Bob, thanks for the info” gains you some points without being a toady.
–If you want to criticize or complain about something, wrap it up in an appealing management bow. “I think I’ve found an opportunity…”, “I think I’ve identified some waste…”. The words “I think” are important, since the boss can then be seeded with the idea and led to believe that they actually have some further constructive insight and are not just being criticized 
–Don’t be flash without substance, don’t pad your work with fluff and shiny things. “Just the facts, maam”, and then just chat afterwards about golf.