As Norman Geisler and Ron Rhodes explain in their helpful book Correcting the Cults, Jehovah's Witnesses believe that only the Father is to be worshiped. They believe that Christ should be shown "obeisance"1 or reverence, but nor be worshiped.
However, as Geisler and Rhodes explain, this is now what the New Testament actually teaches:
"The same Greek word used for worshiping the Father (proskuneo) is used of worshiping Christ in the New Testament. Jesus was worshiped by Thomas (John 20:28), angels (Heb. 1:6), wise men (Matt. 2:11), a leper (Matt. 8:2), a ruler (Matt. 9:18), a blind man (John 9:38), a woman (Matt. 15:25), the women at the tomb (Matt. 28:9), and the disciples (Matt. 28:17). In the Book of Revelation, the worship that the Father receives (4:10) is exactly the same as the worship received by Jesus Christ (5:11-14).2
Most interestingly, as Matthew Slick argues here, the Watchtower Organization at one time taught that Jesus should be worshiped!
Courage and Godspeed,
1. Watchtower, 15 February 1983, 18) as referenced by Geisler and Rhodes.
2. Norman Geisler and Ron Rhodes, Correcting the Cults, p. 166-167.
Article: Sharing the Gospel with Jehovah's Witnesses by Neil Shenvi
Apologetics Interview with Mike Felker by Brian Auten of Apologetics315
Article: A Brief Overview of the Jehovah's Witness Worldview by J. Warner Wallace