Step 1: Recall the conditions for aromaticity.
A compound is aromatic if it satisfies all the following conditions:
(i) Cyclic structure
(ii) Planar structure
(iii) Continuous conjugation
\[
\text{(iv) } (4n+2)\pi \text{ electrons}
\]
This is known as Huckel's rule.
Step 2: Analyze option (1) Pyridine.
Pyridine is a six-membered planar ring with alternating double bonds.
It contains
\[
6\pi \text{ electrons}
\]
which satisfies Huckel's rule for \(n=1\).
Hence, pyridine is aromatic.
Step 3: Analyze option (2) Cyclopentadienyl cation.
Cyclopentadienyl cation contains a five-membered conjugated ring with only
\[
4\pi \text{ electrons}
\]
According to Huckel's rule, systems with \(4n\pi\) electrons are antiaromatic and hence not aromatic.
Thus, cyclopentadienyl cation is not aromatic.
Step 4: Analyze option (3) Anthracene.
Anthracene is a fused aromatic hydrocarbon with continuous conjugation and follows Huckel's rule.
Therefore, anthracene is aromatic.
Step 5: Analyze option (4) Furan.
Furan is a five-membered heterocyclic compound.
One lone pair of oxygen participates in conjugation, giving a total of
\[
6\pi \text{ electrons}
\]
Hence, furan is aromatic.
Step 6: Final conclusion.
Therefore, the compound which is not aromatic is
\[
\boxed{\text{Cyclopentadienyl cation}}
\]
