How do you handle employees complaining about one another?

Tough one - some of it is just gossip.  For this we have implemented a Zero Gossip Policy and we fire for this now.  
Having said this we do 360 reviews - we ask the employees to review their team members.  This gives them a healthy way to give feedback.
At times we have to dig deep and see if some of the comments are valid so we investigate.  Then get back to the person who was complaining and discuss further.

Hope this helps.