What do cockroaches live off of? American cockroaches will eat plants and other insects. Other types of cockroaches feed on almost anything; soap, glue, toothpaste, sugary starchy foods, wallpaper paste and book bindings. As they crawl through dirty areas they are tracking the bacteria and germs into our homes. They contaminate food by shedding their skins which can cause allergic reactions especially in children. Roaches are known to carry over 33 kinds of bacteria including E.coli and Salmonella.