Light micrograph section through human colon tissue showing carcinoid tumour of the colon. Carcinoid tumours are a type of slow-growing cancer that can arise in several places throughout the body. Carcinoid tumours are one subset of tumours called neuroendocrine tumours and are most commonly found in the gastrointestinal tract such as the stomach, appendix, small intestine, rectum and in this case the colon.