Is it common to have a mentor in academia? At a recent networking workshop (not one of the "just don't be an introvert" ones, an actually helpful one with applicable ideas) I learned that it is supposedly very common to have a (career) mentor in academia. 
This is not meaning a supervisor or a former supervisor you are still in contact with, but a person a few years further in their career than you, not necessarily exactly working in the same field but well established and experienced in some aspects of academia and academic careers where the mentee is in need of guidance (networking, public outreach, being from a similar minority, whatever is important to the mentee).

I promptly started to figure out what I would need in a mentor, who could be a good mentor and now how to approach them. But the questions come back nagging, because while this all makes sense and an online research came up with many tips and mentoring schemes I still have never met someone who said they had a mentor in this way.

So the question is: Do people have mentors in academia? If so, what are your experiences as a mentor/mentee? And would it be appropriate to ask someone who you have never met before for an informal conversation because you feel they might just be right for you?
I won't try to guess how common it is, suspecting that it is quite common. But it is very useful in any case. 

But there are two (at least) scenarios. 

The first is that your "mentor" doesn't even know that s/he is your mentor, but you just take cues from them about how to behave in any academic and personal situations that you observe. How do they lecture? How do they respond to questions? How do they interact with colleagues. I've had many mentors of this kind. I was lucky enough to meet up with one of the most important ones later and thanked him for providing the role-model I needed as an academic. He was in the same field, but his research area was very different from mine. 

The second is more personal. This is someone that you specifically interact with, though not necessarily in a research sense. But someone that you are comfortable asking questions of. Even somewhat uncomfortable questions. Someone who you trust will give you good feedback and not be shocked it you ask a strange question that you might not ask a stranger. These relationships are harder to arrange and must, IMO, develop over time. 

The second sort of "formal" mentor can be more instrumental in promoting your career, of course, since they know you well and, having taken on the role, are likely to be supportive when asked. 

If you are a grad student, I strongly suggest that you seek out one or more professionals as mentors of either kind. Even better, is to seek out a circle of people who are mutually supportive - but for the right reasons. People who respect one another and help when they can.