As a leader, how do you handle negative office politics?

Office politics exists only where permitted by the management.  If you don't want politics amongst your team, don't allow it.  If you are open, honest and fair it's hard for politics to thrive.  The key thing is to punish political behaviour by team members, not reward it.   

Obviously you can't prevent politics that affects people at your own level and above.  If you like it, stay and enjoy it.  If you don't, then consider finding a new job.