The basic grammar dictionary lists ことがある, ことができる, ことになる and ことにする as the set phrases which have to use こと, though I don’t know for sure whether or not there are others (such as ones not listed in the basic grammar dictionary – flipping through the intermediate dictionary, for example, reveals ことによる and ことはない).

There are, however, a whole pile of verbs for which using either こと or の is odd, because こと tends to be used when the preceeding clause is astract, while の is used when it’s concrete. So, for example, saying のを考える is basically ungrammatical。