Would it be ethical of a student for him/her to act as a proofreader/editor for other students' essays and homework?

As an student instructor, I would consider it ethical if certain conditions are met:

1. The proofreader isn't taking unfair advantage of the student, especially when paid for his services. There are plenty who call themselves 'tutors' who will use dishonest tactics; for instance, deliberately being unclear as to his editing methods in order to encourage continuing dependence on his services, making false criticisms of edits the student's friend made for free, or emotionally manipulating students who are from abroad.
2. The student isn't taking unfair advantage of the instructor. It's important that the student respects classroom policy on external assistance and observes the relevant boundaries when working with his editor.
3. The editor isn't taking unfair advantage of the instructor. It's not clear from your question whether the editor is in the same course as the writer, or merely at the same school. If the editor is enrolled in the same course, I'd consider it unethical for him to read through other students' work before his own is handed in.
4. The instructor isn't taking unfair advantage of the editor. There should be reasonable office hours to work with students, because that work is the responsibility of the instructor, not the classmates.

I believe it is good practice for students to proofread and edit each other's work. I also believe it is ethical, provided that

1. it is consistent with the professor's instructions,
2. the final product is still substantially the work of the student submitting it, and
3. it is properly attributed.

See, for example, my university's honor code (paragraph IV.C).

I'm going to offer a CS perspective from Germany, which may apply to other engineering fields, as well:

While there is quite some writing in CS, within my circle of academic contacts, we usually go by the rule: A few minor mistakes are sloppy and irritating, but are to be expected in long documents and therefore excusable. What is not excusable is failing to have someone else proofread the document. This is particularly (but not exclusively) true when writing in a foreign language, such as (for us) English.

So, in other words, having someone else proofread each of your more significant documents (theses, seminar papers, ...) is considered a part of due diligence. This is, of course, not limited to student assignments, but will continue during one's professional life - authors of a paper should always give the camera-ready version of a research paper to someone so far uninvolved to do some proofreading, for instance.

In the student context, preferrably, this proofreading should be done by a fellow student:

• They are likely to be savvy about the topic. This reduces the chance of false positives, where they consider something incorrectly written or expressed, which is actually correct in the terminology of the subject at hand.
• It is a good practice for them; like that, they will not just train writing, but also proofreading/correcting, which they will have to do efficiently also later on.
• As all students have to do the assignments, and all students need proofreaders, this allows for inherent compensation to some extent, as students can simply thank each other by returning the favour of proofreading.

As other answers remarked, it is important that proofreading is really that - identify mistakes, point out unclear or confusing statements and document structure, possibly suggest how to improve the text on an abstract level, but do not change anything other than the simplest of mistakes (straightforward typos that leave only one option for correction).

Concerning the attribution, I am undecided on whether it is obligatory:

• It is certainly the polite thing to do.
• In longer documents that feature acknowledgments (such as graduation theses), those acknowledgments provide a good opportunity for mentioning that the author received help by proofreaders. (Of course, not everyone puts acknowledgments in graduation theses; especially when the deadline is closing in, there are more essential parts of the document to work on.)
• Given that proofreading is, as explained above, an indispensable part of writing a document, and a rather "technical" one (just like, e.g., using a text editor), it is debatable whether it should be mentioned. Maybe it should, but in that case, the producers of one's text editing software, or the manufacturer of one's computer, should probably be mentioned just as well, which is rarely done.
• In shorter documents (especially papers with a page restriction), there is most probably simply no space to mention mere operational details of the paper writing process such as proofreading.

To summarize, I have rarely seen mentions of proofreading in documents, even though they occasionally do occur. Especially in student documents, when I do not find any mention of proofreading and I ask the student whether they have had someone else proofread their document, I am definitely much more dissatisfied with the answer "No, that's why I didn't mention it." than with the answer "Yes, of course; having someone else proofread my document before I hand it in is so self-evident that I do not see a point in specifically mentioning it."

EDIT: Whether or not to add an attribution may also depend on cultural customs. I recently brought up the topic concerning one of our papers in my department in Germany, when we had handed out that paper to a few colleagues from other departments for checking comprehensibility and clarity of the text (i.e. not restricted to spellchecking, but actual contents of the paper). My tentative suggestion to add a note in the acknowledgments thanking them for their suggestions was rejected as "silly" by my co-authors, because the colleagues from the other department "have just read the paper and suggested a few minor changes", and because "everyone always gives other people one's papers for external suggestions and those external people are normally never mentioned". People from other cultures might agree on different courses of action that are "normally" followed.