Several types of terrestrial and aquatic worms can be easily grown; look up 'worm farm' to find plenty of information on cultivating earthworms. White worms and black worms can also be grown indoors.
Many insects with aquatic larvae, such as mosquitos, chironomid midges (bloodworms), and chaoborid midges (glassworms), will lay eggs in a bucket of water placed outside. Crush up a handful or two of grass clippings or other vegetable matter in the bucket; this encourages the growth of the protozoans on which the insect larvae feed. Somewhat similar methods can be used with the terrestrial black soldier flies ('phoenix worms) and fruit flies.
As mentioned, livebearers are an excellent source of fry. Some egg-layers such as convict cichlids and fathead minnows are also prolific and easy to breed.
Some kinds of shrimp, such as red cherry shrimp, are reliable breeders. Other easy-to-raise crustaceans include amphipods (scuds) and daphnia.
Crickets aren't too hard, but they do tend to be smelly and noisy. Tropical roaches are easier, silent, and odorless.