Whenever you go to the restroom, say, every hour and a half or so, just sneak into the stairwell (usually located close to the restrooms in large office buildings) and go up and down five flights of stairs. It will take only a couple of minutes, and none of your coworkers will be the wiser.
Five flights is just enough to get your heart beating hard, but not enough to break a sweat, which you don't want to do at the office.
You'll go back to your desk refreshed, alert, and in a better mood. If you feel guilty about taking the extra two minute break, look at it from the corporate point of view: you'll probably be more productive this way.
Sitting for too long has negative health effects, and it may also give you the same kind of rump-itis you get on long distance drives. (Don't look for that disease in medical texts, you won't find it.)
It's also beneficial if you want to lose weight. A number of recent studies have shown that the most important factor in losing weight -- apart from avoiding sugars and starches -- is to keep your metabolism high. That's why short, intense bursts of exercise are actually better calorie-burners than long, slow jogs: they keep your system going for longer after you stop working out. The other way to keep the engine running is to stimulate it every couple of hours with a few flights of stairs.
Don't try to go two stairs at a time, or you'll end up hurting your knees.
Every big office building comes with its own built in StairMaster. Take advantage.