Decide on a policy. Trying to ban affairs at work is probably a mistake. Take a position, make sure it's understood, and stick to it.
Be discreet. Address the issue responsibly - look at each case on its merits and don't intervene unless you have to. It's vital to ensure that neither party to the affair feels unfairly targeted.
Beware the lawsuit. When relationships turn sour, the individuals involved can become vindictive. Make sure there's no room for favouritism or claims of unfair dismissal.
Don't tolerate harassment. There's a big difference between a reciprocal romance and harassment. Treat all complaints seriously but fairly.
Draw the line. In the workplace, there's a fine line between what is acceptable and what isn't. A peck on the cheek, for example, is rarely deemed offensive, but a tonsil-tennis session in the kitchen may well be.
Weigh it up. People will always hook up at work; don't assume it will end badly. Be aware of what's going on, but don't wade in unless you have to.
Look on the bright side. Office romances needn't spell bad news. As long as they don't interfere with efficiency or reputation, they may even have a positive effect. If a couple work in the same environment, they'll have a better understanding of the pressures involved, and can be more supportive when there are problems at work.