I've been known to intentionally mimic a person's accent in order to help them feel more comfortable. Not a friend's accent, mind, but clients. Having a business in the UK helped me hone this skill. And it's not merely in spoken communication; I found that there was Brit-business-speak in writing too. Even just matching the 'music' of my speech to the other person's seems to help.

It's hard to know whether I have natural tendencies to use my ear to attune to different accents, or I just learned it from my years as a speech-language pathologist.