Is one incentive their ability to communicate their perceptiveness to people in their general community?
Are there other incentives?
The principal reason for writing any letter of recommendation is to benefit the person for whom you are writing it. If a student is talented, helping him or her get into a good program is its own incentive. I can't imagine writing a letter with the motive of showing off my perceptiveness.
An additional motive is that others wrote letters for the writer once, and he/she can show gratitude by paying it forward. From David Keyes' excellent essay on procuring reference letters:
Everyone in a position to write a career-changing letter of reference is there by the grace of earlier generations of mentors at school or work who poured their lives into today's writer and then wrote about the results in now dusty letters. The only gifts today's authors expect from today's candidates are those "in kind" or better to be delivered to tomorrow's candidates, in one-way cross-generational equity. Writers have their own rewards in the success of their protégés, and though they will moan to each other about the burden, they recognize that reference letters are key components of an imperfect system that nevertheless is on the whole effective in keeping their discipline healthy and growing.
As others have said, the main incentive is to help the students.
But recommendation letters are also a service to the departments who read them. Your colleagues will read your letters to help them make admissions or hiring decisions.
Moreover, over time, faculty build up reputations for the kinds of letters they write. Faculty that are known to write overly effusive letters (as an extreme example: "best student in five years!" every year) are not taken seriously. On the other hand, a strong letter from someone who is known to write measured but accurate letters has a big impact. So writing perceptive letters is not useful only to the present student, but to future students as well.
The reputation effect becomes more significant (but more entangled with research reputation) as you climb the academic food chain. For graduate admissions, it's fairly subtle. For faculty hiring, it's much more noticeable, because hiring letters tend to come from a smaller pool. For tenure and promotion, where the pool of writers is even smaller, the reputation effect is quite significant.
I guess the best incentive you can give a professor to write you a good letter is to 1) develop a relationship with the professor so that he or she knows something more about you than the grade you earned in their class, and 2) impress them in some way so that he or she has something good to say about you.
I agree with David Ketcheson. My sole purpose for writing letters of recommendation is to help the student. Letters of recommendation are read by committees that read hundreds of them every year, and I want the committee to have a strong impression of the student after they read my letter, not of me.
That being said, my students don't automatically get the "best" or "strongest" recommendation I can write. They get the recommendation they earn. For example, I cannot justify describing a C student as having strong academic potential. I can't write favorably about an undergraduate who signed up for a research project and then never showed up. And, I usually cannot say all that much about students I don't know very well. No matter what, I will take what I know about the student's strengths and weaknesses and try to paint the best picture possible; it just might not be glowing.
In addition to the excellent points others made, it reflects well on a faculty member and a department for their students to be successful. While I primarily write letters for the benefit of the students, it's great to be able to say when recruiting other students, or when talking to the Provost, that our graduates are getting great jobs.
In addition to the other reasons that have been discussed by other answers, many of which are true, there is one more fairly distinct reason: They may some day need a letter in return.
For example, there are often nomination letters for awards, or promotions from students. I've been in the position to write at least three letters for someone who wrote me a letter of recommendation in the past, and while I'd like to think it didn't bias my letter, it certainly made it easier to justify the time and effort that went into crafting it.