Can you build a road on the other side of another player's settlement?
From the official FAQ: 


  Can the roads I build “go through” other players’ settlements
  and cities?
  
  Answer: No. If you build a new road, it must always connect to one of
  your own roads, settlements, or cities.


The inverse situation is also interesting:


  Longest Road - How can I interrupt the Longest Road of a game partner?
  
  Answer: By building a settlement on an intersection within the Longest
  Road. Of course, you have to observe all building rules when doing
  this.