**Core Concept**
Intracranial hemorrhage (ICH) is a life-threatening condition where there is bleeding within the brain. Hypertensive hemorrhage, also known as intracerebral hemorrhage (ICH), is a type of ICH caused by the rupture of small blood vessels in the brain due to high blood pressure. The brain has a complex vascular network, and the blood vessels are under constant pressure from the blood flow.

**Why the Correct Answer is Right**
The most common site of hypertensive hemorrhage is the basal ganglia, which is a region in the brain that plays a crucial role in movement control and coordination. The basal ganglia are supplied by small blood vessels that are prone to rupture due to chronic high blood pressure. The basal ganglia are located deep within the brain, and the blood vessels in this region are under high pressure, making them more susceptible to bleeding. The basal ganglia are also rich in small blood vessels, which can rupture and cause bleeding.

**Why Each Wrong Option is Incorrect**
* **Option A:** Cerebellum - While the cerebellum can be affected by hypertensive hemorrhage, it is not the most common site.
* **Option B:** Pons - The pons is a part of the brainstem, and while it can be affected by hypertensive hemorrhage, it is not the most common site.
* **Option D:** Cerebral cortex - The cerebral cortex is the outermost layer of the brain, and while it can be affected by hypertensive hemorrhage, it is not the most common site.

**Clinical Pearl / High-Yield Fact**
It's essential to note that hypertensive hemorrhage is a medical emergency, and prompt treatment is critical to prevent further brain damage and improve outcomes. The most common symptoms of hypertensive hemorrhage include sudden headache, vomiting, and altered mental status.

**Correct Answer: C. Basal ganglia.**