Definite articles

Question

When to use definite articles. "No tenemos cerdos" (no article), but "Los cerdos son adorables" (article).What's the difference?

Answer

Hola Peter
When it is the subject of the sentence you need the article:
Los cerdos son adorables.
The other sentence is using cerdos with a very general meaning, as a direct object. This is when in English you normally use "any":

No tenemos cerdos en nuestra granja.
We don't have [any] pigs in our farm.

There are lots of sentences with tener + direct object that don't use the article because we are talking about "things that are expected to be owned/general possessions":

No tengo dinero.
I don't have any money.
¿Tienes casa?
Do you have a house?
No tengo coche.
I don't have a car. 
¿Tienes hermanos?
Do you have any siblings?

The omission and presence of the article is something where there is no specific rule I'm afraid, and no clear-cut explanation. 
Saludos
Inma