It could affect your job

As we've already said, there's no law against seeing a workmate! However, you can be fired if your liasion is having a negative effect on your work. Relationships between coworkers are allowed, but they're rarely seen in a positive light by management and staff. Your superiors might worry you'll be less productive, that you'll start bringing your private life into the office, and that you (and other members of staff) will be distracted.  

Tricky situations
If one of you is superior to the other in the company, things could get even more complicated. Management might think that the superior is abusing his or her position. There could be talk of sexual harrassment and fear of an official complaint from the 'victim' if the relationship ends. You could be accused of favouritism should one give the other a promotion, and you'll be scrutinised by your human resources manager and the rest of the staff. Not nice.

Grounds for a transfer? 
It's not uncommon for Romeo and Juliet to be moved to different departments. If you want to avoid an unwanted, and pointed, transfer, you need to be as discreet about your relationship as possible, remain the consummate professional and don't make it easy on the people who will be out to criticise you.