It depends on the collection, most collections should work even if the hashCode of the elements has not been overridden, except collections like HashSet which rely on the element hashCode in order to work properly.
Beware that the hashCode of a collection usually relies on the hashCode of the elements:
Returns the hash code value for this collection. While the Collection
interface adds no stipulations to the general contract for the
Object.hashCode method, programmers should take note that any class
that overrides the Object.equals method must also override the
Object.hashCode method in order to satisfy the general contract for
the Object.hashCode method. In particular, c1.equals(c2) implies that
c1.hashCode()==c2.hashCode()
See: http://docs.oracle.com/javase/6/docs/api/java/util/Collection.html#hashCode%28%29
