Though faculty are often skeptical of student evaluations, research suggests that student evaluations are an effective tool for evaluating teaching. Here is a link to a meta-study that surveys the results of approximately 1500 other studies on student evaluations:
Cashin, "Student Ratings on Teaching: The Research Revisited"
Here are some of the major conclusions of the paper:
Correlation to Exam Scores
In courses with multiple sections and a common exam, there is between a 0.3 and 0.5 correlation between an instructor's evaluation scores and the students' scores on the common exams. The paper notes that it is rare to ever find correlations above 0.5 in the social sciences when studying complex phenomena.
Correlation to Instructor Self-Ratings
When instructors are asked to rate their own teaching effectiveness, the answers they give have approximately a 0.29 correlation with student evaluations. In addition, when instructors are asked to rate how their effectiveness varied over different courses they have taught, the instructor's answers have roughly a 0.45 correlation with student variation in evaluations across those courses.
Correlation to Ratings of Administrators and Colleagues
When instructors are rated by either their colleagues or by administrators, the scores they receive have between a 0.45 and 0.7 correlation with student evaluation scores. Of course, colleagues and administrators might be basing their score on student evaluation scores that they have seen.
However, ratings by trained classroom observers (who have not seen student evaluation scores) also have 0.5 correlation with student evaluation scores.
Based on this research, I think that it is reasonable to take student evaluation scores into account when analyzing the effectiveness of your own teaching. From a particular instructor's point of view, the 0.45 correlation highlighted above has the most relevance: it means that you can tell which courses you did a good job in based on student evaluations.
Of course, there are some other effects that need to be taken into account. Classes full of highly motivated students tend to give higher ratings than classes of reluctant students. Students in advanced courses also tend to give higher ratings than students in introductory courses. If your abstract algebra students consistently rate you higher than your calculus students, that doesn't necessarily mean that you're doing a better job in abstract algebra.
Finally, it should be pointed out in any discussion of evaluating teaching that there is no universally accepted definition of good teaching. You may perceive advantages or disadvantages in your teaching style that the students do not see, and there's no objective way to determine whether you are right. Ultimately, it's part of every teacher's job to form their own opinions on what constitutes good teaching.
Edit: Who graded the exams?
dtldarek asks below whether the correlation between student evaluations and student exam scores might be due to instructors grading their own class's exams.
Cashin's study cites two other meta-studies for the results on exam scores: one by Cohen and one by Feldman. I haven't looked through the Feldman study, but Cohen's meta-study analyzes several methodological features, including who grades the exams. Of the 68 studies that Cohen analyzes, 10 had each teacher grade their own class's exam, 28 had some external evaluator grade all of the exams, and the remaining 30 had some other system (e.g. each instructor grades one question from all of the exams). From Cohen:
The only other methodological variable that correlated significantly with effect size was evaluation bias. The correlation between ratings and achievement was large when an external grader was used or when each instructor evaluated one part of the test for all students. For 10 studies in which achievement tests were evaluated by students' own instructors, the effect size was much smaller.
That is, the correlation between good evaluations and good exam scores is stronger when the exams are not graded by the teacher themselves.