Use a linked list when you need to store iterators into a container while mutating it. E.g. if you are making a super naive LRU cache, you could use a map<K, list<pair<K,V>>::iterator> and a list<pair<K,V>>. This is something you can't do with vectors unless you can guarantee the capacity will never increase.

This is the most useful case of removing from the middle of a container, which linked lists are good at. Intrusive lists are common for this type of thing, instead of actually storing a list iterator.