In our time, the practice is to wear Tefillin during the entire weekday Shacharit service. Since the commandment of Tefillin has its source in the verse "Bind them as a sign on your hand and let them serve as a symbol on your forehead" (Deuteronomy 6:8), on Sabbaths and holidays Tefillin are not put on. The reason for this is that the word "sign" (ot) is also mentioned in the commandment of the Sabbath, as it is written: "The Children of Israel shall keep the Sabbath, observing the Sabbath throughout the ages as a covenant for all time: it shall be a sign for all time between Me and the people of Israel" (Exodus 31:16-17), and one sign (that of the Tefillin) is not placed on another (that of the Sabbath); the Festivals are comparable to the Sabbath.
Customs differ regarding the putting on of Tefillin on Chol ha-Moed (the intermediate days of the Festivals); some people put on Tefillin, while others do not. In Eretz Israel, the practice is not to put on Tefillin during Chol ha-Moed.