Years ago I had an instance where my direct supervisor on a new job did not "get" me at all, nor did I "get" him. Our interaction, communication, even our understanding of each others emails was really off and awkward. I was doing my job well based on guidance from other colleagues, but I was getting really concerned about my boss feeling very "meh" about me and how it would affect my career there. It got to the point where I realized I was trying to avoid contact with him, only emailing him or returning his calls in response to a voice mail or email from him.
After a couple of months I realized I'd better face the fact that this would not go well for me long-term. The only thing I could think of was to do the opposite of avoiding him. I thought maybe if I spent more time with him, like I did with people I liked, I could at least understand the way he thought and communicated a little better. Even if the progress I made was all one-sided, it would be better than the way things were.
So I started willing myself to walk over to his office and respond to emails and voice mails in person. It wasn't easy at first. In meetings I would force myself to sit in the seat right beside him, the way you would with a friend. After a few weeks, things started to change. When I went over to talk to him I felt comfortable asking about things in his office that were genuinely interesting to me. We started to be less awkward and actually started to build a real ease with one another. I was shocked to discover that he had a funny sense of humor. He remained a pretty reserved guy so it's not like we never sat around and played poker together or anything, but we did achieve a genuine, relaxed easy flow of communication with one another over time, that I really appreciated. A few years after he retired I was looking to move on myself. I called him and asked if he would be a reference for me. The recruiter I was working with later told me that the reference he gave me was one the most positive, glowing references that he had ever had for any candidate during his career.
I never forgot this approach. I've used it deliberately since then with someone I had to work with on a team, but didn't particularly like very much. It worked in a similar way and definitely helped build rapport.
What's the most creative way you've ever built rapport or improved a relationship with a boss or co-worker?