If a student needs a reference letter for graduate admissions or that sort of thing, some profs will ask the student to write a reference letter for themself before sending it off to the prof for minor edits and finalization.
Some profs lie, cheat and steal as well...occasionally in their professional life. Just because a practice is common does not make it right.
This seems to be a somewhat common practice given that some graduate schools ask for several letters of recommendation even when it is not reasonable for the student to have developed deep connections with that many professors, and that most professors are just too busy to write quality letters for all the students that ask them to.
It is certainly "reasonable" to ask for several letters of recommendation for graduate admissions. That many students will not have had substantial personal contact with faculty is something to keep in mind as one progresses through an undergraduate program. Also connections need not be especially deep in order to result in a good letter: if the writer can be confident that the student will succeed in the graduate program she is applying for, that is enough. Often a truly outstanding performance in a single course is sufficient.
Is it acceptable to write most of the reference letter and have the prof make minor edits?
No, this is a form of plagiarism and academic fraud. What you pass off as your written word must actually be yours except where you explicitly document to the contrary.
Do academic institutions frown upon this practice?
Many of them do, yes.
Would it be considered an academic offense if a student wrote a reference letter for themselves and had a prof sign it?
It depends on the institution and probably the nation in question but in the United States: yes, it certainly could be. If I found out that this happened in an application that I read, I would at the very least throw out the entire letter; I would probably be inclined to dismiss the entire application. I would probably not contact the faculty member because in my view they are equally culpable (if not more so because they should know better), but I would be much more skeptical of letters coming from that person and even that institution in the future.
The above takes a hard ethical line, as I am very frustrated with other answers to this and related questions that seem resigned that one must accept unethical behavior in this situation. But here is a different kind of answer:
A graduate admissions letter that a student writes for herself is going to be a bad letter compared to a "real" letter written by a qualified faculty member. A graduate admissions letter is a communication between one mature academic and another: how would a 22 year-old young adult know how to write such a letter in a convincing way? Without having read hundreds or thousands of other similar letters, how would she know what the faculty want to hear? She wouldn't. If you write your own letter, you are at best forging an ineffectively written letter. Surely you deserve a better one?
As for faculty being very busy: yes, we are. As for having lots of letters to write: yes, we do. But writing such letters is part of our job, so a faculty member who does not take time out to write a good letter is not a good faculty member, at least not in this aspect. Writing a good recommendation letter usually takes several hours and often more than one sitting.
How can you help your professor write a good letter (on their own!):
1) Give them lots of time to write the letter.
Academics are busy, and our schedules are uneven. If you give me something to do six weeks in advance, then maybe in week three I'll find a spare afternoon and be able to do it. Leaving much less than a month for someone to write a letter is getting off on the wrong foot and already implicitly asking for less than the best possible letter.
2) Provide information about yourself rather than waiting for the faculty member to ask.
You should not write the letter yourself, but you should certainly include all information that you think might be pertinent, and you are well within your rights to highlight certain information that you think might be especially pertinent. Preparing something like a CV but tailored for a good letter rather than a job would be ideal.
3) Do everything in your power to minimize the attendant clerical work in submitting the letter.
Faculty members are busy and also, honestly, a bit lazy/snooty about routine work. If you tell me to mail a letter to a certain address, then there is going to be a whole day in which I print out the letter and don't get around to correctly putting it in an envelope. If the letters still need to be mailed (fewer and fewer do, and most but not all faculty members prefer to do things electronically), it would be wise to provide a self-addressed stamped envelope. If the submission is electronic, again try to ensure that the faculty member needs to do as little as possible. Ideally we get a website and a password, we enter those in, and we immediately upload the letter. Much more than that is asking for trouble. My own university makes faculty members jump through many more hoops to submit a letter, and this worries the hell out of me.
3') If your letter needs to be sent to multiple locations in a way which requires the faculty member to do something multiple times, see if you can figure out a way for the faculty member to submit the letter only once. E.g., perhaps there is an administrative assistant (AA) at your institution that will agree to receive the letter and take care of the nitty gritty of sending it to various places. You may have to ask for this, and you should ask, as nicely as you possibly can. Given the choice between getting a faculty member to do this clerical work and getting an AA to do it, you want the AA to do it: they are superior in every way. Always remember to be extra nice to the AA's: you want in fact to be nicer to them than the average person they have to interact with, as then they will notice and do better work for you than the average person they have to interact with. If you're asking an AA to do something which it is not absolutely clearly part of their job description, go ahead and ask but be extra extra nice: a small gift at the end is a classy move.
4) Don't be shy about checking up on the faculty member to see whether the letter has been written.
I frankly expect this, to the extent that if you ask me for a letter (including giving me all the information) and never check back again, I almost believe that you changed your mind and didn't really need it after all. It is totally acceptable to ask multiple times for the faculty to turn in the letter. I'm afraid that there has been "email alert inflation" in recent years, to the extent that if I only get one email about something, it feels almost optional. Really important things have a way of resulting in multiple emails coming at shorter and shorter intervals. Even to get me to write my grant reports they are not shy about sending several. You should always be nice about this -- at any point the faculty member could in theory change their mind -- but we are grateful if it is your mental energy which is being spent on making sure it gets done.