Over the years, I have been a manager to a lot of people, which gives me sufficiently big sample size from which I can draw some conclusions. Without a doubt, I would say taking a coaching style and active interest in developing the capabilities of my staff has paid the most dividends, both in terms of a personally rewarding relationship and the long term contribution of the employee to the company.
I guess I developed my coaching style very early on. Back in high school, I realized I had skills and knowledge that was pretty advanced (in terms of software development), and it felt natural to try to share that. I collaborated on the development of some student management software with one of the teachers (representing what I believe to be an early example of "paired programming"), I did a little personal computer tuition on the side, and I taught a class or two on games development to some of the younger students.
Once I joined the workplace semi-officially (during industrial placements between university terms), I found myself appointed team lead among other interns. And it wasn't long after graduating that I found myself a manager of other full-time staff.
One of the advantages of taking self-development seriously (whether learning professional skills, management skills, or new technologies), is that I found I continually added to the stock of knowledge and experience that I could share with others. Also, I found, if (as a student) you pay attention to how something is taught, as well as what is taught, it is easier to pass on the knowledge to others later on.
The trick I find to coaching is to be supportive of a direct report when the opportunity arrives. Care must be taken to not appear to be a "know it all" or come off as condescending. It is better to give the employee a framework or fresh perspective on how to tackle a problem, but let them choose how or whether to use it to address their problem. When done correctly, the employee's capabilities improve as a result, and trust in the manager-employee relationship is strengthened.
Closely aligned with a coaching style is a deliberate approach to delegation. While the manager should never shirk their responsibilities to prevent a train wreck, in most circumstances the employee can be empowered to propose and/or make a decision (particularly if they are on the same page as the manager, which is common following a coaching session).
I found it takes some inner strength, sometimes, to see the process through to its full conclusion. Employees that receive good coaching often attract the attention of "higher-ups". And yet a manager can blow their relationship with the employee if they try to "take back" some of the glory. That's why, as a manager of managers now, I try to acknowledge the contribution of the manager, when I suspect an employee's performance has been helped. Positive reinforcement of the coaching process is the best way to ensure its continuance across the company, ultimately establishing it as part of the culture.