Christians believe in the Trinity. This is the idea that whilst there is one God, he contains three personalities: the Father in heaven, the Son Jesus, and the Holy Spirit who replaced Jesus in the world after he ascended into heaven.
Since Christians see Jesus as the incarnation of God - God made man - they are required to worship him, and in doing so are worshiping the Father and the Spirit.
In the early days of the Church there was much debate over Jesus' status in the Trinity, and some Christian groups today have different views (such as the Unitarian Church).
The majority of Christians, however, follow the Nicene Creed (statement of belief) which describes Jesus as, "Light of Light, true God of true God, begotten, not made, being of one substance with the Father." and talks about the Holy Spirit "who with the Father and the Son together is worshiped and glorified".
The Orthodox Churches have a slightly different view of the Holy Spirit from that held by the Catholic and Protestant Churches, but all of them believe that Jesus should be worshiped.
See Wikipedia for the intricate details