Family is a very special and heart-warming subject, which is why knowing how to speak about your beloved ones in Spanish is a must! Shall we begin?
La familia más cercana - The closest family
| En español | In English | 
| La madre | Mother | 
| El padre | Father | 
| El hijo | Son | 
| La hija | Daughter | 
| El hermano | Brother | 
| La hermana | Sister | 
| El hermanastro | Half-brother, stepbrother | 
| La hermanastra | Half-sister, stepsister | 
| El abuelo | Grandfather | 
| La abuela | Grandmother | 
| El nieto | Grandson | 
| La nieta | Granddaughter | 
| El bisabuelo | Great - grandfather | 
| La bisabuela | Great - grandmother | 
| El tatarabuelo | Great - great - grandfather | 
| La tatarabuela | Great - great - grandmother | 
La familia más lejana - Distant family
| En español | In English | 
| El tío | Uncle | 
| La tía | Aunt | 
| El padrastro | Stepfather | 
| La madrastra | Stepmother | 
| El padrino | Godfather | 
| La madrina | Godmother | 
| El primo | Cousin (male) | 
| La prima | Cousin (female) | 
| El cuñado | Brother-in-law | 
| La cuñada | Sister-in-law | 
| El sobrino | Nephew | 
| La sobrina | Niece | 
| El suegro | Father-in-law | 
| La suegra | Sister-in-law | 
| El yerno | Son-in-law | 
| La nuera | Daughter-in-law | 
La familia en plural - Family in plural
| En español | In English | 
| Los padres | Parents or Fathers | 
| Las madres | Mothers | 
| Los abuelos | Grandparents or Grandfathers | 
| Las abuelas | Grandmothers | 
| Los tíos | Uncles | 
| Las tías | Aunts | 
| Los suegros | Parents - in - law or Fathers-in-law | 
| Las suegras | Mothers-in-law | 
| Los consuegros | Your son-in-law/daughter-in-law's parents or fathers | 
| Las consuegras | Your son-in-law/daughter-in-law's mothers | 
| Los primos | Cousins (male) | 
| Las primas | Cousins (female) | 
| Los hermanos | Siblings / Brothers | 
| Las hermanas | Siblings / Sisters | 
| Los gemelos | Twins (male) | 
| Las gemelas | Twins (female) | 
| Los hijos | Sons or children | 
| Las hijas | Daughters | 
Expresiones varias - Miscellaneous expressions
| En español | In English | 
| Tener hermanos | To have siblings | 
| Ser hijo único | Te be an only child (male) | 
| Ser hija única | To be an only child (female) | 
| Ser adoptado | To be adopted | 
You will love it
That was an official list, however in the section About Spanish I have prepared for you an article Family members in Spanish - did you know these funny facts? in which I describe family-related Spanish words that you won't find in the textbooks.