Step 1: Apoptosis is programmed cell death executed largely through the activation of caspases.
Step 2: The dominant pathway in most cells is the intrinsic (mitochondrial) pathway, which is governed by the balance of pro-apoptotic and anti-apoptotic Bcl-2 family proteins.
Step 3: When pro-apoptotic signals prevail, mitochondrial outer membrane permeability increases and cytochrome c is released into the cytosol.
Step 4: Cytosolic cytochrome c binds APAF-1 to form the apoptosome, which activates initiator caspase-9, in turn activating executioner caspases-3 and -7.
Step 5: Because this central control point and release of pro-apoptotic factors occur at the mitochondrion, it is regarded as the principal organelle in the execution of apoptosis.
Conclusion: The answer is option 3, mitochondria.