You can buy lady-bug beetles through the mail, for instance. Release them in the garden, and they go after the aphids, et cetera. They have no adverse side effects. Personally, I've never bought any. I just provide a wide habitat of plants and hope they show up.
Bats are great natural mosquito controls.
So are many kinds of birds. Bees, of course, are important pollinators every garden needs. Some of our readers swear that by placing a bird feeder near their garden, many of their pest problems disappeared. The birds were eating the grubs and snails and insects. I don't want to sound like a broken record, but compost and mulch are great helpers.