In Hartshorne's chapter on Weil divisors he fixes the following hypothesis:
$(*)$ Every scheme is Noetherian , integral, separated, and regular in codimension 1
I can understand why you would want the first three hypotheses, but the regularity in codimension 1 is a little mysterious to me. What is the motivation behind this hypothesis? Is there any geometric reason, or does this just make the algebra in this chapter easier? For reference, regular in codimension 1 means that any local ring of $X$ of dimension 1 is regular.