We told my parents and DH's parents both times.

DH's parents live 10hrs away and DD was the first grandchild on that side and was also born on DH's dad's birthday. As we didn't know the date until a couple of weeks before delivery date my parents were in Perth when DD was born and didn't get to see her until she was a week old.

With the twins DH's parent had to get here the day beforehand so that they could look after DD for us until DH could get home late in the evening on the night they were born.