Final answer:
Organelles unique to animal cells include the centrosome, containing centrioles, and the lysosomes, which break down waste. Plant cells typically do not contain these organelles.
Step-by-step explanation:
The organelles that can only be found in animal cells and not in most plant cells are the centrosome and lysosomes. The centrosome is a structure that plays a crucial role in cell division and contains a pair of centrioles, which are not present in plant cells. Additionally, lysosomes, which are often referred to as the cell's 'garbage disposal', are responsible for breaking down waste materials and cellular debris. Plant cells typically manage these processes in vacuoles, hence lysosomes are not common in plant cells.
While both plant and animal cells have microtubule organizing centers (MTOCs), only animal cells have centrioles associated with the MTOC in the complex known as the centrosome. Moreover, despite the eukaryotic cell's highly compartmentalized structure, certain organelles like lysosomes and centrosomes are unique features of animal cells, facilitating specific cellular functions such as waste management and cell division.