Final answer:
Ribosomes can be found free floating in the cytoplasm or attached to the rough ER, playing a crucial role in protein synthesis within the cell.
Step-by-step explanation:
The organelles that may be found free floating in the cytoplasm or attached to the endoplasmic reticulum (ER) are ribosomes. Ribosomes are essential for protein synthesis within the cell. These small organelles are either attached to the rough ER, making it appear 'bumpy' due to their presence, or they are found as free ribosomes within the cytoplasm. Free ribosomes synthesize water-soluble proteins, while those on the rough ER make proteins for export or insertion into cell membranes. Ribosomes are not surrounded by a membrane, making them unique compared to other organelles like mitochondria, Golgi apparatus, or lysosomes, which all have specific membrane enclosures.