I actually trained to be a teacher (7–12) and now teach at the college level and to adults. I am a gifted public speaker (which comes naturally, but is only part of the mix). I think the features of a good teacher also include a personal interest in lifelong learning (as stated above) and an incredible inate sense of curiousity.
However, I think Rozee nailed it with the above description of the other half of the equation-the student(s). Some students are very easy to teach (probably the ones who are natural born teachers and who possess the characteristics I mentioned—curiousity, etc). Other students are incredibly difficult to reach, motivate, and/or inspire and, as Rozee noted, it takes an incredible amount of work to be the detective that will figure out what makes it click for THAT student.
I also believe that some folks do well in the educational environments we create and, for others, these environments spell the death nell for curiousity, interest.
I am also trained to teach Gifted and Talented students and feel most comfortable solving the mysteries of how to reach the more brilliant kids and help them connect dots between what appear to be unlikely things (e.g., math and music). I must admit that I get bored out of my head teaching average and below-average students. That tells me that they are probably pretty bored as well. But I have seen less promising students suddenly make a connection with a particular piece of information and have found that can be used to their advantage (e.g., they like spiders, so we read books about spiders).
So, yes, I think some people are born with SOME of the features to be a GOOD teacher buried deep in their bones someplace. There are a number of other aspects of being a gifted teacher that take experience, mentoring, and lots of practice to master.