Why do Peter and Zara Phillips have no title?

Princess Anne, their mother, wanted to shield her children from the publicity that titles such as Prince and Princess might bring. They are the first grandchildren of a sovereign to carry no title.
However, they are not the first children of a princess to carry no title. The children of Princess Alexandra, the Queen’s cousin, who were born in the 1960s, are also untitled.

On another note:

Even though they do not have titles they are still in line of succession to the throne. However, as Peter Phillips, the Queen’s eldest grandson, is engaged to a Roman Catholic, he may have to give up his place in the line of succession to the throne.

The 1701 Act of Settlement bars monarchs and their heirs from becoming or marrying Catholics. Under the Act, Peter will be required to renounce his right to the throne – he is 10th in line at present – or Miss Kelly will have to formally give up her membership of the Church.