Razib makes a good point in his response to the ScienceBlogs question: "What makes a good teacher?" I think he could make the #1 reason more inclusive by modifying it to say: "A semester's worth of psychometrics, covering individual differences in intelligence and personality." So, even if you have to teach students who aren't bright nor highly conscientious, you know how to relate to them, exploit whatever motivations / interests they have, etc.
The only two popular takes on students who are bettered by awesome teachers are: 1) the elite prep school group Razib mentioned, bright & enthusiastic, for whom the gardener-teacher supplies the necessary extrinsic stimulation to allow the full flowering of their minds (Dead Poets Society); and 2) children of tragedy, whom the alchemist-teacher transforms from would-be dead-enders to knowledgeable captains of their own ship (Dangerous Minds).
In reality, most students are bored to tears by school, since most of it is geared to promising students (i.e., bright & enthusiastic). The average or below-avg students get frustrated b/c the material is over their head -- often ridiculously so w/ Constructivist or Socratic methods that require the student to figure out the pattern themselves & then state it explicitly or apply it elsewhere. Such progressivists are unaware that they've just administered something like the Ravens test, the most highly g-loaded one out there. Four years worth of such pupil-dilatingly frustrating instruction is enough to turn off anyone. Here in Montgomery County, MD, the current public high school geometry textbook is all but devoid of formulas for the students to memorize or refer back to, w/ only question marks where the budding Einstein should have figured out the formula on their own and stored it in memory -- since writing it down over top of the taunting question mark would not only be destruction of school property, but would forever ruin the self-discovery journey for all future owners of the defaced book.
The same is true of "learning for learning's sake" approaches -- not everyone scores high on Openness to Experience on the "Big Five" personality scale. Pleading -- and then badgering -- Closed students to explore the abstract beauty of math, rather than giving them practical tools they can use (like calculating rate of increase/decrease of prices), is like struggling to bring out the inner Extrovert from an inveterate Introvert in acting classes.
Kids are not all easily tutorable fledgling conquerors of the fields of life, nor are the remainder mere lumps of clay awaiting transformation by the teacher's Abracadabras and waves of the hand. Most students can sense who the idealistic teachers are, and they eat them for fucking breakfast. While not as Oscar-level inspirational as other methods, I prefer to relate to kids on their own level -- occasionally that means playing the gardener-teacher role to a promising student, but more often that means breaking the awful truth to them that life isn't fair, that there are some things you have to learn in order to function as a job-holding adult, and that large parts of formal schooling should just be viewed as their day job that they tolerate until they get to do what they really want. And for most of them, these visions of the future don't include more academics -- quite the opposite.
So, you motivate them by stop lying to them that all of this material will be vitally important further on. Still, regardless of where they end up, better grades and completion of high school will demonstrate one's work ethic. And a larger vocabulary will always be worth more than a miniscule one -- whether to impress whoever's interviewing you, to deal a delicious diss to someone who's annoying you, or to stand out from the crowd when trying to talk to girls (although brains don't necessarily make a girl more desirable). The same is true of other subjects, especially foreign languages. No student will take a teacher seriously who suggests that there's an inherent beauty and intrinsic merit to studying foreign languages -- perhaps for the teacher, but not for the typical student. Again, a more realistic approach is called for: knowing even rudimentary Chinese will help in a future where China will be a big global economic player; or for the blue collar, learning Spanish if immigration trends continue. More, your average high school boy would rather clip out his own tongue w/ rusty gardening shears than master a second tongue, but once Spring Break in Rio approaches, he's suddenly engrossed in a Teach Yourself Brazilian Portuguese book. The two greatest motivators: survival and reproduction.
In sum, whatever other commendable qualities a good teacher may have, foremost must surely be an honest, hard-headed approach to one's noble calling. Steve recently voiced a similar opinion on how to best utilize male-typical & female-typical talents for good government. The fundamental error of those striving to be good teachers -- and god knows I was one of them! -- is the two-part belief that: 1) all students are inherently the same in intelligence and motivation, so all apparent variation is due to environmental variation; and 2) moreover, all students are like the teacher in intelligence & personality, so what appeals to and would motivate the teacher would transfer easily to the case of the students, if only after some minor adjustments for age differences, etc. Alas, both of these hypotheses have zero empirical support -- and after all, that's what really counts in judging a good teacher: who effectively leads the kids toward the brightest future that each is capable of attaining and in the least painful way possible? Quasi-religious beliefs that serve more to make teachers feel good and pure about themselves, rather than serve the needs of the students, are the very antithesis of good teaching. In light of a century of psychometric research on personality & intelligence, honest reflection on the part of good teachers requires that we abandon the fallacy that all students are equally above-average blank slates.