To be aromatic, a compound must satisfy three conditions:
-There must be a delocalised π-system containing
4n+2;n∈N electrons (i.e. alternating double and single bonds).
-All electrons which contribute to the π-system must be in the same plane (i.e. no puckered rings).
-Contributing electrons must be arranged in at least one ring.
Structures such as benzene:
Clearly obey these conditions.
Yes, you can have a cycle with more double bonds, such as cyclooctatetraene:
However, this does not meet the requirements for aromaticity due to it's 8 electrons in a π-system. We actually call compounds with
4n;n∈N electrons (along with the other aromaticity requirements) antiaromatic. Antiaromatic structures are incredibly unstable, meaning compounds such as cyclooctatetraene pucker out of the plane to avoid this:
The structure with double bonds is almost always more useful.
Not necessarily, they just don't form an aromatic system.