A rule-of-thumb for recognizing aromaticity is in counting the number of delocalized electrons--if they equal (2n+2), where n is an integer, then the molecule is likely aromatic. This is referred to as Huckel's Rule.
Benzene, C6H6, was recognized as the first aromatic hydrocarbon, with the nature of its bonding first being recognized by Friedrich August Kekulé von Stradonitz in the 19th century. He envisioned the delocalised electons rapidly shifting configuration between one of two forms, or resonance structures, in which double bonds rapidly move about the hexagonal ring. However, the total strenth of the aromatic bonds involved in aromaticity is stronger than the total strength of the bonds when formulated as a combination of single and double bonds. Aromatic bonding, therefore, must be recognized as a type of bonding distinct from other types of multiple bonding, such as double or triple bonds. This can be described more quantitatively with molecular orbital theory.
Napthalene, consisting of two coplanar six membered rings sharing an edge, C10H8 is another aromatic hydrocarbon. Its smell is familiar to those who have encountered mothballs.
Some important arenes are called PAH (Polycyclic Aromatic Hydrocarbons). They are compounds composed of 4-7 benzenic rings. A very famous PAH is the benzoapyren (known for its cancerogenic and teratogenic properties). Other are the anthracen or the fluoranthen.
Phenol is a common arene.