I'm not sure whether I should really post these few thoughts of mine because they do not directly address the question as it was asked but every time somebody starts talking about students evaluations I feel a strong urge to say something like that, so why not now and here? As usual, I believe I'm guilty of violating the "no discussions on MO" rule, so feel free to downvote.
I find the current system of term end student evaluations extremely counterproductive. On one hand, most students are just plainly incompetent to answer many of the typical questions (like "rate your professor's knowledge of the subject"). On the other hand, it creates an unhealthy situation when instead of getting a constructive criticism during the course when the adjustments can easily be made, we just get emotional comments on our performance when it is too late to do anything and more often than not in the format that is impossible to interpret in any reasonable way. Out of each 50 evaluations I got only 3 or 4 contained something that I could use to adjust my teaching. The rest either contained pure rating numbers that didn't tell me anything I hadn't known myself already (yes, I did know if the topic was hard or easy, I did know whether I prepared my lectures carefully or just improvised, etc.) or the comments like "This is the best teacher ever!" or "He should be fired immediately!" (sometimes I got both in the same class), which also carried no real content whatsoever.
I agree that it is a great idea to get the feedback from the students and I admit that some students may be afraid to express themselves openly, but it would be much better just to have a small forum type website for each course where every enrolled student would be able to publicly post any concerns or comments about the course in a free style format as soon as they arise with or without signing it (both options should be available) and the teacher would be able to read those and to respond and decide whether any action/adjustment is due. Such records would also tell much more about everybody's teaching to any promotion committee or whoever else who might have a real interest in what is going on.
Technically it is not so hard but I've never seen anything like that done. Instead, we have that system of meaningless average numbers of subjective ratings of rather poorly defined things. Indeed, what is my "being organized", or "preparedness", or "willingness to help"? I believe I can read and speak basic English but I'm just unable to assign any meanings to such general words, much less to assign a numerical value to the qualities they are assumed to represent. I understand the sentences like "You never returned homework #2" or "Your lecture on continuity was very clear", but not the sentence "Your overall preparedness was 5 on the scale from 1 to 10".
The most unpleasant thing is that the administration tends to take those numbers rather seriously sometimes. I don't care: I've got my tenure and my salary is high enough but it is a pity to see young people who are afraid to teach $\varepsilon-\delta$ in calculus courses because it may irritate the students and result in bad evaluations.
As to the requested background information, I'm currently a full professor of mathematics at University of Wisconsin-Madison but I spent more than 10 years at Michigan State University before that. In Michigan we were required to do evaluations for every course taught; Wisconsin requires just to do them "now and then" (not less than one in 3 semesters or something like that; I still have to figure the exact rule out). I wouldn't say they were taken very seriously by the faculty in either place but I cannot speak for everyone. I have never tried to figure out who wrote what for the lack of time and curiosity for such things but I believe Leonid that it may be possible to do in a small size class.