A few years ago I would have thought this was might be relevant to people teaching large courses of undergraduates in the humanities. However, I was wrong. Unfortunately, experience has shown that plagiarism does occur, even in physics courses, and at the graduate level. There are cases of students submitting Ph.D proposals and literature reviews that involve cutting and pasting text from papers and the internet. Although certainly not confined to them this can be more of a problem with students from non-Western countries. There do seem to be some "cultural" differences as to what is acceptable practice and what is not. This does not excuse it, but does mean that sometimes first-time offenders need to be gently cautioned and educated.
A range of offences can occur, ranging from sloppy referencing to blatantly copying large swathes of text and presenting them as ones own.
So if you don't use Turnitin (or something equivalent) try it. You won't know if there really is a problem until you check.
If you do detect plagiarism make sure you report it to the relevant academic authority. Do not just give the student a private warning. It is important that someone is keeping track. Otherwise repeat offenders may not really understand the severity of their offence and get appropriately disciplined.
Another issue, which is harder to detect, is that of ghost writing.