A list keeps order, dict and set don’t: when you care about order, therefore, you must use list (if your choice of containers is limited to these three, of course 😉 ).
dict associates each key with a value, while list and set just contain values: very different use cases, obviously.
set requires items to be hashable, list doesn’t: if you have non-hashable items, therefore, you cannot use set and must instead use list.
set forbids duplicates, list does not: also a crucial distinction. (A “multiset”, which maps duplicates into a different count for items present more than once, can be found in collections.Counter — you could build one as a dict, if for some weird reason you couldn’t import collections, or, in pre-2.7 Python as a collections.defaultdict(int), using the items as keys and the associated value as the count).
Checking for membership of a value in a set (or dict, for keys) is blazingly fast (taking about a constant, short time), while in a list it takes time proportional to the list’s length in the average and worst cases. So, if you have hashable items, don’t care either way about order or duplicates, and want speedy membership checking, set is better than list.