Good question. It seems to be used commonly with abuela. Here is a book titled "La Abuela/Grandmother."

<http://www2.loot.co.za/shop/product.jsp'lsn=8420433012>

In his article about translating the prose-poetry of María Rosa Lojo, Brett Alan Sanders says this:

In "The Structure of Houses", my work benefits from a knowledge of Lojo's own history. For "la abuela" I translate "Grandmother", capitalized and without the ambiguous definite article, since the allusion here-according to Lojo herself-is to her own grandmother.

Let's see what the native speakers say.

Good question, but maybe you should ask the opposite: why "papá" doesnt have an article? Any family relationship demands some sort of article in general:

La abuela...
El tío...

Without them, it sounds as if "abuela" and "tío" were first names. However, "papá" and mamá" are words as special and unique as their own real names names. I've never called my father by any other word in my life, so I guess they are felt almost as proper names, and therefore, they tend to be used without the article; at least when they are your own fathers.

Without the article, "abuela" in that sentence sounds unacceptable to my ears.

Thanks!! "Dad" and "Grandma" carry basically the same personal "feel" in English, so I guess that was why I expected a corresponding similarity in Spanish.

Natasha said:

Thanks!! "Dad" and "Grandma" carry basically the same personal "feel" in English, so I guess that was why I expected a corresponding similarity in Spanish.

True, but "grandpa" is not "abuelo". The word "abuelo" is "grandfather", and I don't think you normally say:

Grandfather comes today.

There are some affectionate names for "grandfather" in Spanish, but none as common as "grandpa" in English (other than "abuelito", etc., but it is not the same as "papá").