My experience has been that plagiarism happens pretty frequently in any class where the assignment isn't structured in a sequenced way that makes it pretty difficult to do. A class that only has a final research paper at the end has been usually the worst. Most universities subscribe to a service like Turnitin to try to scan for violations. And in the last several years, it's been particularly an issue with Chinese students (my university has seen a huge influx of students from China), partly I think because of the pressures to be perfect, the emphasis being put on getting the grades and credential rather than a recognition of needing to gain skills for post college life, and because such corruption is rampant even among professors/business circles in China. There's been a lot of exposure of faked scientific research from China which has led to a drop in international research partnerships. To be fair, within the Asian cultures, much of what we consider plagiarism in research is considered normal procedure there. Not the exam cheating sort of plagiarism, but the lack of citation for others' work kind.

Usually it's the prof's discretion about how to pursue, but there are Univ policies that vary and make it a royal pain to execute.