Step 1: Understanding C$_3$ symmetry.
A molecule has a C$_3$ axis if it can be rotated by 120° to give an identical structure.
Step 2: Applying to the structures.
Structure I has a threefold rotation due to three identical methyl groups.
Structure III, with symmetrical substitution, also maintains a C$_3$ axis.
Structure IV has three identical substituents arranged symmetrically, also giving C$_3$ symmetry.
Structure II lacks this symmetrical arrangement.
Step 3: Conclusion.
Thus, compounds I, III and IV possess C$_3$ rotational symmetry.