Thinking over some recent posts that relate to this idea (starting with this one), my experience of the mentor business popped up from my dark recesses. It was the early 1980s when I was active in youth ministry (small Bible study groups, Sunday School teaching, youth camps, etc) that I do believe I was a mentor to a young Christian fellow, just a few years younger than I was.
We didn't use that term, of course, the minister just asked if I'd work through some studies with Zeke. I did, for a few weeks; quite a few weeks, actually. I picked him up from his place and we went to my place for study, chat and prayer. It was a real friendship, we talked about work, girls, plans, hopes. I was impressed by his sagacity.
I moved into the city, he didn't and we drifted apart. But, it was a great (and now that I've remembered it) and memorable experience.