**Core Concept**
The pancreas contains various types of endocrine cells that produce hormones regulating glucose metabolism, and endocrine tumors can arise from these cells. The most common endocrine tumor of the pancreas is associated with the production of a specific hormone.

**Why the Correct Answer is Right**
The most common endocrine tumor of the pancreas is an insulinoma, which is a benign tumor producing excess insulin. Insulinomas arise from the beta cells of the islets of Langerhans in the pancreas. The excess insulin production leads to hypoglycemia, which is the primary clinical manifestation of insulinoma. The pathophysiology involves the unregulated release of insulin, which can be life-threatening if left untreated.

**Why Each Wrong Option is Incorrect**
* **Option A:** Gastrinoma is a type of endocrine tumor that produces gastrin, leading to peptic ulcers and diarrhea. While gastrinoma is a pancreatic endocrine tumor, it is less common than insulinoma.
* **Option B:** Somatostatinoma is a rare type of endocrine tumor that produces somatostatin, leading to diabetes and gallstones. It is not the most common pancreatic endocrine tumor.
* **Option D:** Glucagonoma is a rare type of endocrine tumor that produces glucagon, leading to hyperglycemia and a skin rash. It is also not the most common pancreatic endocrine tumor.

**Clinical Pearl / High-Yield Fact**
Insulinomas are typically benign and can be cured by surgical resection. However, they can be challenging to diagnose due to their small size and ability to produce excess insulin.

**Correct Answer:** C. Insulinoma. Insulinoma is the most common endocrine tumor of the pancreas, characterized by the production of excess insulin.