Step 1: Recall the distribution of MHC Class I molecules.
MHC Class I molecules are expressed on
\[
\boxed{\text{All nucleated cells}.}
\]
Their function is to present endogenous peptides to CD8\(^+\) cytotoxic T cells.
Step 2: Eliminate the incorrect options.
• Antigen-presenting cells express both MHC Class I and Class II.
• T lymphocytes are not the only cells expressing MHC Class I.
• Mature red blood cells lack a nucleus and therefore do not express MHC Class I.
Hence,
\[
\boxed{\text{All nucleated cells}}
\]
is the correct answer.
Therefore,
\[
\boxed{(C)}
\]
is the correct answer.