So there's this couple in the office who are sneaking around and you've heard about or suspect it. What do you do? Well, gossip is always fun, isn't it? Try to resist. It's just a mean thing to do and a time waster. If the couple is trying to hide it, sit down with one or both and let them know that you're really happy for them, but their actions are having an impact on the workplace. Don't be accusative; try to be a helpful friend. Tell them you don't want them hurt by speculative gossip. They need to act professionally in the office. Tell them to read the section above and to talk with HR if they are unsure of the office policy. They'll appreciate your honesty and you might get invited to the wedding.
If you're watching a breakup, that's tough. Do your best not to take sides - even if one person is being a real jerk. Consider your relationship with the parties and if you are a (close) friend be there to listen, but take every opportunity to remind them that the office isn't the place for emotional tsunamis. If he or she can't keep it together, get away from the office for a while. Be sympathetic and supportive, but out of the office. You can do this in an empathic way. Not "Your behavior is inappropriate and unprofessional." Try "I can see you are upset and I think it would be better if you went home (or to a coffee shop, or for a walk) until you feel better."
There are going to be some circumstances where you are going to have to get help. If your friend seems unduly depressed, or his or her lover appears to be retaliatory or a stalker, take the issue to HR asap.