While some insects fall firmly under the heading of pests, there are also some that are quite beneficial to keep around. Research what kinds of insects are local to your home and figure out which ones to protect and even encourage. Beneficial insects, like bees, attack the pests and feed off plants in a good way. To help encourage this, plant as many native varieties of plants as you can, and really mix it up. A large variety of plants and flowers attracts a battalion of beneficial insects.
Aside from bees, some kinds of beetles, wasps, spiders, earthworms and ladybugs are all great to have around, to name a few.