God has one will, and Jesus Christ has two (one being the Divine will of God, while the other being a human will). This was settled in the Sixth Ecumenical Council, Constantinople III. The Letter of Pope St. Agatho, read during the Fourth Session of the Council, says
...we confess the holy and inseparable Trinity, that is, the Father, the Son and the Holy Ghost, to be of one deity, of one nature and substance or essence, so we will profess also that it has one natural will, power, operation, domination, majesty, potency, and glory... our Lord Jesus Christ himself is both perfect God and perfect man, of two and in two natures: and after his wonderful Incarnation, his deity cannot be thought of without his humanity, nor his humanity without his deity. Consequently, therefore, according to the rule of the holy Catholic and Apostolic Church of Christ, she also confesses and preaches that there are in him two natural wills and two natural operations. For if anybody should mean a personal will, when in the holy Trinity there are said to be three Persons, it would be necessary that there should be asserted three personal wills, and three personal operations (which is absurd and truly profane).
St. Agatho's letter neatly deals with the question: there is one will in God, the Lord Jesus has two wills, and the three Persons certainly do not each have an individual will. The Acts of the Council clearly state that
...we likewise declare that in him are two natural wills and two natural operations indivisibly, inconvertibly, inseparably, inconfusedly, according to the teaching of the holy Fathers. And these two natural wills are not contrary the one to the other (God forbid!) as the impious heretics assert, but his human will follows and that not as resisting and reluctant, but rather as subject to his divine and omnipotent will.
Jesus, God the Son, assumed a human will, along with human nature, at the Incarnation. This human will was perfectly subject to the Divine will, and by assuming it, Jesus redeemed it. We see this submission firsthand:
"And he withdrew from them about a stone's throw, and knelt down and prayed, saying, “Father, if you are willing, remove this cup from me. Nevertheless, not my will, but yours, be done.”"
-Luke 21:41-42 (ESV)