Popular projects usually attract the most attention and political game playing. You'll have more room to maneuver and will have to spend only a fraction of your time playing politics. Do a favor for someone and you'll find that you add to your political capital and create a more positive place to work. Obviously you can't always choose your co-workers, but whenever possible you can volunteer for projects with people you trust. The more time you spend with those people the less time you'll have to worry about politicking.
Every organization has people who get stuff done without knifing anyone else in the back.
Keep your eyes open for these people and learn everything you can from them. Cultivating the leaders of your organization will create opportunities for you. But to do your job you'll have to also cultivate secretaries, janitors and all those people who govern how things really get done in organizations. No organization is politics-free, but there are organizations where politics plays a minor role. If things at your company seem truly irremediable, it might be time to start looking.