[Skiznibbler]

At first I read that an aromatic compound is a compound that contains a ring with alternating double bonds in which the electrons are delocalized and the ring exhibits a greater stability than regular conjugated systems. That makes sense to me.

In Organic Chemistry by Clayden I read something different. In this book they say an aromatic compound is any compound that contains a benzene ring or other ring of atoms. Is that correct? If I'm not mistaken some rings have double bonds between their carbons and are not conjugated systems. Can an aromatic compound be a compound with a non conjugated ring system? In other words is any old cyclic compound considered an aromatic as long as it has a ring somewhere?

[azmanam]

no, any compound with a ring is not necessarily aromatic.  you need 4n+2 electrons delocalized in a planar cyclic ring of pi orbitals.

some aromatic ring (use wiki for structures)

cyclopropene cation
cyclopentadiene anion
tropyllium ion
naphthalene
indole

These structures may or may not jive with your understanding, but all are aromatic.

[Arkcon]

No, aromatic systems have a number of differences.  For one thing, they undergo different reactions, as aromatics are more resistant to conditions that will react with an ordinary cyclo-compound.  Also, from X-Ray crystalography studies, we can see that all C-C bonds in benzene (or C-N, or C-O; for heteroaromatics) are shorter than either a C-C bond or a C=C (or heteroatom bond) is.