You can exclude the subject pronouns when the ending is sufficient to convey the person. Both the singular and plural forms of the second-person ending are always unique, so there's never a need to use the subject pronoun 'tú' (notice the accent mark) or 'vos' (used in some areas instead of 'tú', having another conjugation that also has a unique ending) or 'vosotros, -as' (the plural form).
In the present indicative tense, both the singular and plural forms of the first-person ending are always unique, so there's never a need to use the subject pronoun 'yo' or 'nosotros, -as' (the plural form).
The same holds true for the preterit tense.
In the imperfect tense, the singular first- and third-person endings are identical, so the subject pronoun needs to be used to establish the person (once established, the subject pronoun needn't be repeated). The plural first-person subject pronoun is unique, so there's no need to use 'nosotros, -as'.
Both the singular and plural third-person endings in all tenses are shared by three different subject pronouns (él, ella, usted and ellos, ellas, ustedes). It is therefore necessary to use the subject pronoun to establish the person (once established, the pronoun may be omitted).
Soy, somos, eres and sois uniquely convey the person. Except to give emphasis, the subject pronouns are not required.
Es and son do not uniquely convey the person. The subject pronoun must be provided at least once to establish the person.
Have a look at the verbs hablar, comer and vivir, which are not irregular, and you'll see that the same explanation will work for them as well.
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