Zakaat cannot be given to one’s ascendants. That is, to one’s parents, maternal and paternal grand-parents and even great grand-parents. In the same way, Zakaat cannot be given to one’s descendants. That is, to one’s children, grand-children, great grand-children, etc. In the same way, the husband and wife cannot give Zakaat to each other.
Apart from the above mentioned, it is permissible to give Zakaat to all other relatives such as one’s brothers, sisters, nephews, nieces, maternal and paternal uncles and aunts, step father or step mother, step grandfather, father-in-law, mother-in-law, etc. (obviously this is when they are eligible to receive Zakaat).
Furthermore, it is mentioned in a Hadith that by giving charity to one’s relatives one receives double reward- one reward for giving charity, and one for showing kindness (joining ties) to one’s relatives.