The "Work Spouse": Harmless Flirting or Slippery Slope to Harassment?

CNN informs us of the phenomenon known as the work spouse.

If you were an employer/manager and saw this sort of relationship developing between two of your employees, what would you do? To what extent are you concerned about the relationship going too far or falling apart and resulting in tension, reduced productivity, or harassment claims/liability? To what extent would you think it important not to interfere with your employees' personal (but perhaps not, strictly speaking, "private") relationships?