Can I place a bridge that has no hope of completion?
From the Carcassonne FAQ:


  Q: I have memorised all the tiles.  Am I allowed to play a tile when I know that by doing so I am creating a space which can never be filled, either because the required tile doesn't exist or because all the possible tiles have already been played?
  
  A: Yes, that is permitted. But be aware that, if by doing so, you have prevented your opponents from finishing a road, cloister or city (especially a Cathedral city!), they may seek revenge!


I know I've had my fair share of putting pieces that make it impossible for other players to complete a large city they've invested several meeples into.  Bonus points if multiple players are fighting for the city and you make it impossible to complete, therefore cutting down their meeple supply and taking away precious points in the end!