Step 1: Understand apoptosis.
Apoptosis is a programmed and regulated form of cell death that occurs naturally in multicellular organisms. It helps maintain tissue homeostasis and remove damaged or unwanted cells.
Step 2: Identify major features of apoptosis.
Typical characteristics of apoptosis include cell shrinkage, chromatin condensation, membrane blebbing, and fragmentation of DNA into smaller pieces.
Step 3: Analyze option (A).
Endocytosis is the process by which cells internalize substances from the external environment. It is not a defining feature of apoptosis. Therefore, option (A) is incorrect.
Step 4: Analyze option (B).
Uncontrolled cell proliferation is associated with cancer and abnormal cell growth, not programmed cell death. Hence, option (B) is incorrect.
Step 5: Analyze option (C).
During apoptosis, specific enzymes called endonucleases cleave DNA at regular intervals, producing characteristic DNA fragmentation. Thus, option (C) is correct.
Step 6: Analyze option (D).
Cell migration refers to movement of cells from one location to another and is unrelated to the core mechanism of apoptosis. Therefore, option (D) is incorrect.
Step 7: Final conclusion.
Hence, DNA fragmentation is a characteristic feature of apoptosis.
\[
\boxed{\text{DNA fragmentation}}
\]
Therefore, the correct answer is option (C).