Some of the most common foods that Jamaicans eat are brown-stewed fish, jerk chicken and coconut chips. Jamaicans use spices such as allspice, pimento, ginger and nutmeg to flavor many different foods that they eat. Seafood is consumed often by the average Jamaican, with fish and shellfish like shrimp, lobster, tuna, mackerel, snapper and jackfish being plentiful in the surrounding waters. Continue Reading.