The most common insect pests in the United States vary by region. You might not be plagued by the same sorts of bugs if you live out in the country as you would be if you lived in the city. Fortunately, most pest insects in the United States are more annoying than they are truly dangerous. Nevertheless, nobody likes to share his home with a bunch of uninvited creepy crawlies. The best way to avoid most common pests is to keep your house neat and tidy and not to leave food sitting out where bugs can get to it.
Cockroaches are very common pests in big cities. They like to live in warm houses and especially kitchens where they can find food and crumbs to eat. They are nocturnal and usually come out only at night. Roaches aren't dangerous and don't carry disease, but they look really gross. They are pretty big and they can run fast.
Ants are very common all over the United States in both urban and rural settings. They usually build their nests in your yard in warm, dry soil or under pavement, then enter your house at night to look for stuff to eat. Some ants that live in warmer climates like Florida, Texas or Southern California are known to sting, although this sting isn't really dangerous unless you are allergic. The best way to avoid ants is not to leave food out for them.
Bed bug infestations are a relatively recent phenomenon in the United States and bed bugs are probably the most dreaded of household pests. They sleep in your bed sheets during the day, and then come out at night to bite you and suck your blood as you sleep. Bed bugs aren't known to carry diseases, so the bites aren't necessarily dangerous. They do itch very badly though. Bed bugs are extremely difficult to get rid of.