One type of circulatory system that animals can have is the open circulatory system. In this system, the blood is not always contained within blood vessels. Instead, it flows freely through cavities in the body and comes in direct contact with the organs.
An example of an animal that has an open circulatory system is a grasshopper. The blood of a grasshopper circulates throughout its body, helping deliver nutrients and remove waste, but it doesn't stay in tubes the whole time like in a closed system.