**Core Concept**
The appendix is a small, tubular structure attached to the base of the caecum. It is a common site for various types of neoplasms, with some having distinct clinical and pathological features. The most common tumour of the appendix is a type of neoplasm that arises from the mucosal lining of the appendix.

**Why the Correct Answer is Right**
The most common tumour of the appendix is a carcinoid tumour, which is a type of neuroendocrine tumour. Carcinoid tumours of the appendix are typically small, well-differentiated neoplasms that arise from the argentaffin cells of the mucosal lining. They are often discovered incidentally during surgery for appendicitis or appendiceal mass. Carcinoid tumours of the appendix are usually benign and have a low risk of metastasis.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is not specified, but it is not the correct answer. Carcinoid tumours are the most common tumours of the appendix, not other types of tumours.
* **Option B:** This option is not specified, but it is not the correct answer. Other types of neoplasms, such as adenocarcinomas, can occur in the appendix, but they are less common than carcinoid tumours.
* **Option C:** This option is not specified, but it is not the correct answer. Other types of tumours, such as lymphomas, can occur in the appendix, but they are less common than carcinoid tumours.
* **Option D:** This option is not specified, but it is not the correct answer. Other types of neoplasms, such as sarcomas, can occur in the appendix, but they are extremely rare.

**Clinical Pearl / High-Yield Fact**
Carcinoid tumours of the appendix are often discovered incidentally during surgery for appendicitis or appendiceal mass. They are usually small and have a low risk of metastasis.

**Correct Answer: C. Carcinoid tumour**