I feel particuarly strongly on this matter, as I have seen it happen in a number of my favourite shows. Obviously the actors have a strong chemistry, and a relationship could develop, but I find that when that relationship breaks down, and still has to be portrayed on the screen, it can make it awkward not only for the actors involved, but for the fans knowing that somehow, real life has tainted the relationship, and can turn people off of a show.
When it comes to love and dating and couples, I really couldn't care less what people do, where and how it started, and what each person is into. When it comes to loving someone you have to do whatever it is that makes you comfortable and happy. That's alll and there's nothing more.
Out there in the world, couples are getting together all the time. It makes no difference if they are a private couple or celebrities, who has any interest in who gets together with who except the couple themselves? If they make a good TV couple, it stands to reason they might want to get together in real life, but the public don't need to know about it - it isn't that interesting. Who would be interested if Joe Bloggs next door gets a new girlfriend?
If people are couples on television shows and become couples in real life, I figure that's their business; although it should also be permitted with their contract (if that's an issue). That being said, they should think about the fact that it might impact their work relationship if they end up breaking up. It could potentially be difficult for them to work together as an on screen couple after a real life break-up. But, it's pretty much their business.