There are several avenues you can take to get rid of bugs and insects without resorting to chemicals. For example:
You can use vinegar (white or apple cider) and dish soap to catch house flies.
A baking soda and sugar concoction has been known to attract cockroaches (via the sugar) and eliminate them (via ingesting the baking soda).
White vinegar, pepper, cinnamon and fresh mint are just a few of the ingredients in your kitchen that can either repel or eliminate ants.
If you have a severe infestation, consider calling in a pro.