Concept:
According to Hückel's rule, a cyclic, planar and completely conjugated system is aromatic if it contains
\[
(4n+2)\pi
\]
electrons.
A system containing
\[
4n\pi
\]
electrons is antiaromatic and therefore lacks aromatic character.
Step 1: Examine option (A).
The cyclopentadienyl anion contains
\[
4+2=6\pi \text{ electrons}
\]
\[
6=4(1)+2
\]
Hence, it satisfies Hückel's rule and is aromatic.
Step 2: Examine option (B).
The heterocyclic anion also possesses
\[
6\pi \text{ electrons}
\]
and satisfies
\[
4n+2
\]
electron count.
Therefore, it is aromatic.
Step 3: Examine option (C).
The cyclooctatetraene-type ring contains
\[
8\pi \text{ electrons}
\]
\[
8=4(2)
\]
Thus it does not satisfy Hückel's rule.
Hence, it lacks aromatic character.
Step 4: Examine option (D).
The fused polycyclic aromatic hydrocarbon possesses a conjugated aromatic \(\pi\)-electron system and exhibits aromatic character.
\[
\begin{aligned}
(A) &: \text{Aromatic } (6\pi) \\
(B) &: \text{Aromatic } (6\pi) \\
(C) &: \text{Lacks aromatic character } (8\pi) \\
(D) &: \text{Aromatic}
\end{aligned}
\]
Therefore,
\[
\boxed{\text{Option (C) lacks aromatic properties}}
\]
Hence, option \(\mathbf{(C)}\) is correct.