I have an idea for a website, which I'm afraid may land me in trouble. I want to create a website where students from the university I attend can submit exams that they took (with scores of 90% or above), and they will be publicly posted on the site for other university students to utilize and study from. However, would this cause any violation of academic dishonesty rules? Would the professors try to hunt me down and get me suspended from the institution?
Of course, we don't know what your university's academic dishonesty rules say. But in most cases they are pretty broad, and there is probably a clause that could be interpreted to include your website, if your university's authorities decide to do so. I think the odds are good that there will be at least one professor who is upset enough to push them to do something about it. They might just try to get you to take the site down, they might try something harsher. There's no way to know.
In general, I think most professors are aware that students may be informally sharing their exams with one another. For that reason, they usually change exams from term to term, and if they reuse questions, do so only after several years. However, some may be startled to see it done as systematically as you propose, and try to stop it.
I am not a lawyer, nor do I know your local laws, but posting an exam on your website would probably violate the copyright of the professor who wrote it (unless you have his or her permission). This would be another avenue someone could pursue if they wanted your website gone.
Finally, professors could try to prevent their students from posting their exams on your website. For example, they might stop letting students keep their graded exams. Or, they could add a line to their syllabus that "you may not share your graded exams with anyone", on penalty of failing the course or academic dishonesty sanctions. This could not only deprive your website of material, but also make it so that students can't even share their exams informally anymore, which I assume is contrary to your goals.
This depends greatly on your university policies. It could result in some serious formal problems for you which could haunt you for a long time.
Regardless of the policies, I think it is simply inappropriate to do this without the teachers' permission. While I do take extra care to never re-use questions on my exams, others do not and they could easily consider the exam their intellectual property. Whether or not there is any validity to their claim is not really the issue. The fact is that some will feel this way and because of those feelings they will be very unhappy with you.
I think a better solution would be to offer a prep site where previous questions are analyzed and then new questions are proposed which are similar but not identical - that is they would depend on the same knowledge base and thinking skills. There should be no reason a teacher would complain about this (in fact, I would think the teachers would be quite happy about this as it would help students to better prepare for the exams).