The dynamic at my workplace is a little weird.
I work in a small machining and fabrication shop. (I'm described as having "A white-collar mind and blue-collar hands". I love the shop environment, it suits me very well.) Our lead hand, Jamie, is not well-liked by most of the other shop floor workers; this is kind of typical of this industry. Everyone hates the lead hand because he's in charge and has to deliver sometimes unpleasant orders to the other workers. I always have had the attitude "You don't have to like it, you just have to do it." While Jamie and I don't see eye-to-eye on some things, we get along well enough. I respect his knowledge, which he's been very generous with, and I have learned a lot from him. We aren't "friends" per se but we do have a good working relationship, and make a good team.
It certainly doesn't hurt me to be nice to Jamie but as the other shop workers started to see how Jamie and I work well together, and that he treated me far less abruptly than he did the other shop floor people, rumours abounded that we must have more than a "work" relationship, if you know what I mean. The fact that it's common knowledge also that I'm in a relationship with Anthony (who used to work there) only added fuel to the fire, because Jamie and Anthony hate each other with a fiery passion.
The rumours got out of hand to the point where Jamie and I were both called up on the carpet by our boss, who fortunately believed us when we both firmly denied we were anything more than co-workers. The boss had never said anything about the relationship between Anthony and I, because while we didn't actively hide anything or lie about it, we acted professionally at work and it was never an issue, but our boss felt that all the gossip flying around about Jamie and me was getting out of hand and causing problems. He couldn't have inappropriate relationships causing disruptions in the shop, of course.
Whenever either of the two shop hands who were mostly responsible for the gossip would suggest there was anything going on between Jamie and me, I would just shrug and say, "That's news to me," or "Wow, you seem to know more about my love life than I do!" I refused to let them get a rise out of me, and I refuse to participate in gossip of any kind because of things like this. Even though it may start out harmlessly enough, in the long run it can be very damaging to someone's career.