Any organism with a diet that consists chiefly of insects and similar small creatures is an insectivore.
Although individually small, insects exist in enormous numbers and make up a very large part of the animal biomass in almost all non-marine environments. In Queensland pastures, for example, it is normal to have a greater total weight of scarab beetle larvae under the surface than of the beef cattle grazing above it.
A great many creatures depend on insects as their primary diet, and many that do not (and are thus not technically insectivores) nevertheless use insects as a protein supplement, particularly when they are breeding.
The biological order Insectivora includes a number of mammals which happen to be insectivores, but there is no necessary link. Just as many members of the order known as Carnivora are actually omnivores (and one, the Giant Panda, is a herbivore), several members of the Insectivora do not eat insects.
Some examples of insectivores include nightingale, swallow, gambusia (also known as mosquitofish), carp, frog, lizard, bat, and spider. Insects also can be insectivores. Examples would be dragonflies, hornets, ladybugs, and praying mantises.
Insectivorous plants also exist, including the Venus flytrap, several species of pitcher plants, butterworts, and sundews. They are generally native to poor soils that lack nitrogen, which they obtain by trapping insects.