Being a new Ph.D. advisor, I spend a fair amount of time thinking about what makes a good adviser. I was very fortunate to have a great advisor as a student (after I switched out of the lab of the crappy one I started with). My advisor (Prof. Mentor) always took time to help me when I was intellectually stuck. His enthusiasm about science was infectious and no matter how demoralized I was when I stepped into his office, I came out charged up to wrestle my project into submission. I received wonderful training on how to recognize where the cutting edge of my field was and how to formulate questions to test ideas on that front. I learned a lot of my philosophy on what type of scientist I want to be from discussions with him about different approaches to science that people take. I learned that the cutting edge was not necessarily synonymous with the most popular research areas. Most importantly, Prof Mentor gave me the freedom to develop my own questions and did not micro-manage (micro-managing always brings me to a halt with a mule-like stubbornness that I am unable to control). There is not a day that goes by that I do not find myself in some situation asking myself what Prof Mentor would do. But even when I was a student, I understood that while he was the perfect advisor for me, other students in the lab thought he was an awful advisor. They felt that he ignored them, that he gave them no direction. They floundered, never latched onto a project, or became convinced that their project was fatally flawed. Several of them dropped out of the Ph.D program. As I talked to more and more of my labmates about why they were unhappy, it became clear that my perfect Prof Mentor really was a bad mentor - for them. What was a perfect amount of intellectual freedom for me was a lack of intellectual guidance for them. What was a blessed lack of micro-managing for me was a lack of management at all for them. It is always easy to dismiss those who fail in situations where others succeed as "not having the right stuff", but many of the people who dropped out were smarter than me.
In some ways it's really too bad that there isn't an on-line "dating" service like "Matchmakers" for student advisor relationships. How great would it be for both student and adviser to know in advance that they were simply incompatible!