**Core Concept**
The pancreas is a complex gland with both exocrine and endocrine functions. Endocrine tumors of the pancreas are rare but can be benign or malignant, affecting the production of various hormones such as insulin, gastrin, and vasoactive intestinal polypeptide (VIP).

**Why the Correct Answer is Right**
The most common endocrine tumor of the pancreas is a **gastrinoma**, which is a type of neuroendocrine tumor (NET). Gastrinomas are usually located in the duodenum (the first part of the small intestine) but can also occur in the pancreas. They secrete gastrin, leading to excessive acid production in the stomach, causing symptoms such as peptic ulcers and diarrhea. Gastrinomas are often associated with the **multiple endocrine neoplasia type 1 (MEN1) syndrome**.

**Why Each Wrong Option is Incorrect**
**Option A:** Insulinomas are rare endocrine tumors of the pancreas that secrete insulin, causing hypoglycemia. While they are significant, they are not the most common type.
**Option B:** Glucagonomas are also rare endocrine tumors that secrete glucagon, causing hyperglycemia and a characteristic rash. They are not the most common type of pancreatic endocrine tumor.
**Option C:** Somatostatinomas are rare endocrine tumors that secrete somatostatin, causing symptoms such as diabetes and gallstones. They are not the most common type of pancreatic endocrine tumor.

**Clinical Pearl / High-Yield Fact**
The Zollinger-Ellison syndrome, caused by gastrinomas, is characterized by severe peptic ulcers, diarrhea, and abdominal pain. It is often associated with the MEN1 syndrome.

**Correct Answer:** C. Gastrinoma