There are five indoor types of cockroaches. These pests can spread diseases if they get in your food. Mice are simply looking for a good place to find a bite to eat. If you have a mice problem, you need to get rid of them immediately, as they can spread diseases and even their urine or feces in your food and the places you lay your food. These creatures can be as large as a foot or more in length.
Termites live in wood.
They like eating wood, too. You may never even know you have a problem, if you don't look for them specifically. They cause problems when they eat the wood that holds your house together. There are many different types of ants that like eating many different types of things. But you'll likely only have ants in your home if you have food out lying around.