Remember that damages is not the plural of damage, but actually has a different meaning.

Damage means “loss or injury to a person or property”. It is an uncountable singular noun and has no plural form.

E.g.: The cost of the damage to the US caused by Hurricane Ike was estimated at USD 18 billion.

Other words you could use instead of damage: loss, injury

Damages means “money claimed by, or ordered to be paid to, a person as compensation for loss or injury”. It is an uncountable plural noun and has no singular form.

E.g.: The Claimant wishes to sue Acme for damages as a result of a loss sustained by the Claimant after Acme’s failure to perform its obligations.

Other words you could use instead of damages: compensation, satisfaction

I most frequently read sentences where the writers use damages where they mean damage. It is also common to confuse the two meanings.

More examples:

WRONG
In order to understand properly the rules concerning civil liability insurance for damages caused to a person (e.g. death, injury or health breakdown), it is essential first of all to present the general rules of Polish law relating to civil liability for such damages.

RIGHT
In order to understand properly the rules concerning civil liability insurance for damage caused to a person (e.g. death, injury or health breakdown), it is essential first of all to present the general rules of Polish law relating to civil liability for such damage.

WRONG
If a party is in breach of a warranty the other party can terminate the agreement and sue for damages caused by the breach.

RIGHT
If a party is in breach of a warranty the other party can terminate the agreement and sue for damages to compensate for any loss or injury caused by the breach.

WRONG
Any person whose trademark right has been infringed or any person authorised by act of law, may demand the cessation of the infringement, the surrender of unlawfully obtained profits, and compensation for damages according to the general principles of law.

RIGHT
Any person whose trademark right has been infringed or any person authorised by act of law, may demand the cessation of the infringement, the surrender of unlawfully obtained profits, and compensation for damage according to the general principles of law.

BUT – and here’s an exception…

English-speaking lawyers do sometimes use “damage” in the plural to refer to multiple losses or injuries. This is an exceptional use of the word, unique to legal jargon, and breaks the rule that “damage” is an uncountable singular noun. In everyday English “damages” can only mean compensation or satisfaction.

Summary

Damage = loss or injury to a person or property (uncountable singular noun)
Damages = money claimed by, or ordered to be paid to, a person as compensation for loss or injury (uncountable plural noun)

BUT
Damages (rare legal meaning) = multiple losses or injuries to a person or property