- "approximate" grade breakdown (no mean, median, or standard deviation, so there is no comparison to other students, this doesn't necessarily mean fixed grading)
- no information at all (note at many institutions this might actually be bad. Please see the answer to a related question by AndrewC for a full explanation about how this could work)
- full distribution (can create a competitive environment plus privacy concerns)
- limited statistics (special care has to be taken such that the ones you provide are not misleading, and again comparisons are being made to some central tendency, see Chris Cunningham's answer for a full explanation)
- no information at all (can potentially lead to grade anxiety if the students are at an institution with a grade obsessed culture - although this can work well in the right setting)
Explanation + Past Experience:
I have done three things is the past.
I gave just the median and standard deviation
I gave a histogram, with rough rough grade cut offs. See (3)
I gave the median and "rough grade cutoffs." I explicitly warned that these grade cutoffs are only guidelines for approximately where you stand in the class and not your actual grade on the test. For example I might give the following cut offs "A: >88, B: >75, C: >60, D: >40". I then say "These are not your actual grades, only approximate grades based on, roughly, how much I would expect an A, B, C, and D student to have learned the material." In addition, I explicitly say "The entire class will be curved, at the end, so note that there are ways that the average of your 'approximate letter grades' on these exams could potentially be lower or higher than your final grade (but this is rarely more than by a +/-). This is a very rough curve for you to gauge where you are at. No +s or -s are mentioned because this would give a false sense of accuracy." I also put this warning in the syllabus.
I found that students much preferred options (2 and 3 about equally) to option (1) because two and three give them a better idea of what your expectations are, and it also relieves some of their anxiety about not knowing what their grade is at. If you go this route, definitely don't forget to put the warning in your syllabus. This protects you with documentation in case a student were to complain to the administration about the average of their exam grades being slightly higher than their final grade. However, I have never had a student complain about this; they understand that the grade cutoffs are innacurate and are only presented as a service to them and that if they are close to a border line, they understand that they could be sitting at the lower grade.
The histogram is an option that could potentially add information to the grade cut-offs but while it does add information I think it has serious drawbacks. The reason why I prefer "approximate but slightly inaccurate grade breakdowns" to the histogram method is that I don't want to create a competitive environment. I like to frame the test results in language that emphasizes what I expected them to learn, rather than a class rank (even though these things are highly correlated). I did sense some added competitiveness when using the histogram (although it wasn't a huge effect), so I think I'm not going to do it in the future. Note, several academics often mention the competitive nature of math classes as a reason for the lack of women and other underrepresented groups in mathematics. Because of this, in the future, I am no longer going to tell students the median. I would, especially, not recommend giving out the full distribution, because in addition to the reason above, it might be possible to figure out who scored what with some investigative work on the students end. I also think the full distribution would convey a false sense of certainty.
One might ask, well given the last paragraph why don't you know the grade breakdown in advance (i.e. fixed grading). The answer to this is, when writing a new test every year, with new, sometimes creative problems, I never know all the possible mistakes students will make until afterwards. Weighing the mistakes I see and looking at the distribution, I then identify the "approximate cut offs".
Lastly, I'd really like to try not providing any information. I think if you create an atmosphere where grades are completely de-emphasized, and reinforce that the student's holistic performance will be used to determine a grade at the end of the course, this could work very well. If a student is anxious about where they sit in terms of grades, they could ultimately request a meeting with you to discuss what they need to work on and what they are doing really well. Unfortunately, the bureaucracy at my large University, and the general grade anxiety in a class of mostly freshman who earned 4.0+ GPAs in high school, makes creating this environment difficult. If you do go this route, you also need to explain it clearly, and in detail on your syllabus, and keep some form of documentation of student performance so that you can justify all your grades.