I found 4 passages in which such worship directed to Jesus appears in the NT and discovered that the English word "worship" each time expresses one Greek word - προσκυνέω, proskyneō aka proskuneo.
John 9:35 - Jesus heard that they had put him out, and finding him, He said, "Do you believe in the Son of Man?"
36He answered, "Who is He, Lord, that I may believe in Him?"
37Jesus said to him, "You have both seen Him, and He is the one who is talking with you."
38And he said, "Lord, I believe." And he worshiped (proskuneo) Him.
Revelation 5:11 - I heard the voice of many angels around the throne and the living creatures and the elders; and the number of them was myriads of myriads, and thousands of thousands,
12saying with a loud voice, "Worthy is the Lamb that was slain to receive power and riches and wisdom and might and honor and glory and blessing."
13And every created thing which is in heaven and on the earth and under the earth and on the sea, and all things in them, I heard saying, "To Him who sits on the throne, and to the Lamb, be blessing and honor and glory and dominion forever and ever."
14And the four living creatures kept saying, "Amen " And the elders fell down and worshiped (proskuneo).
Revelation 19:10 - Then I fell at his feet to worship (proskuneo) him. But he said to me, "Do not do that; I am a fellow servant of yours and your brethren who hold the testimony of Jesus; worship (proskuneo) God. For the testimony of Jesus is the spirit of prophecy."
Revelation 22:8 - I, John, am the one who heard and saw these things And when I heard and saw, I fell down to worship (proskuneo) at the feet of the angel who showed me these things.
9But he said to me, "Do not do that I am a fellow servant of yours and of your brethren the prophets and of those who heed the words of this book. Worship (proskuneo) God."
How does this relate to Rome? Roman dogma specifically endorses and approves the bowing down in a religious context to non-deity entities such as the Blessed Virgin, saints, and angels. Roman apologists contend that the Bible contains examples of people bowing down to other people, and it seems to be perfectly OK. Tim Staples has said:
Is kissing or kneeling down before a statue the same as worshiping it? Not necessarily. Both Peter in Acts 10 and the angel in Revelation 19 rebuked Cornelius and John, respectively, specifically for worshiping them. The problem was not with the bowing; it was with the worshiping. Bowing does not necessarily entail worship. For example, Jacob bowed to the ground on his knees seven times to his elder brother Esau (Gen. 33:3), Bathsheba bowed to her husband David (1 Kgs. 1:16), and Solomon bowed to his mother Bathsheba (1 Kgs. 2:19).Another prooftext Roman apologists use is 1 Chronicles 29:20 -
Then David said to all the assembly, "Now bless the LORD your God." And all the assembly blessed the LORD, the God of their fathers, and bowed low and did homage to the LORD and to the king.For the record, all of those OT verses mentioned save 1 Kings 2:19 use a form of proskuneo in the LXX.
Protestants respond in numerous ways, one of which is to remind the Romanist that these occurrences are not in a religious context. To greet someone or to show honor to the king is clearly not worship. I've pointed this out myself at length. Romanists respond that this distinction is not as hard and fast as we make it sound.
"See?" they say, "It's permissible to proskuneo non-divine entities."
Now, it occurred to me the other day that The Watchtower Bible and Tract Society, the Jehovah's Witnesses, often experience the same allergy to throwing proskuneo around that we as Protestants do. But of course, it's a bit of a different animal for them, since JW dogma is henotheistic in nature. But if Jesus Christ were to receive worship as divine, then would that not weigh in favor of our contention that Christ is Himself Jehovah?
Consider James White's debate with on-again, off-again, now in good standing, now in poor standing JW apologist Greg Stafford. White mentioned the passages I printed above from Revelation 4 and 5, where the Lamb and the One seated on the throne are recipients of proskuneo from the beings surrounding the throne.
Dr. White plays a clip from his debate with Stafford starting at minute 23:15 of this video. You can hear Stafford insist that the proskuneo of the aforementioned passage does not apply necessarily to the Lamb, that is, Christ, in this scenario. Perhaps it is only the One seated on the throne, the Father (or Jehovah on Stafford's view), Who is receiving the proskuneo of the creatures and elders, etc, in this scene. Obviously, if Christ were to be on the receiving end of a proskuneo act and accept it as proper, the JW view would be seriously damaged, as such worshipful actions are due and properly rendered to Jehovah alone.
Read the passage through from Revelation 4 to the end of 5 and it becomes clear that there is no disjunction between the worship given to the Father and that given to the Lamb - Christ. Thus - zing! - the worship Christ receives is identical to that which the Father (Jehovah Himself on the JW view) receives. And the Father never objects, never corrects those who are worshiping, and neither does Christ. Thus John 5:22-23 is pictured as fully realised in the heavenly scene:
22"For not even the Father judges anyone, but He has given all judgment to the Son, 23so that all will honor the Son even as they honor the Father. He who does not honor the Son does not honor the Father who sent Him.Thus, a useful weapon in the Christian's arsenal of arguments against Watchtower dogma is hamstrung on Roman Catholicism, as RC apologists try to justify their actions towards statues of dead people and angels by attempting to show that it's OK to proskuneo non-divine entities.
Catholic Answers seems not to see this:
The 1950, 1961, and 1970 editions of the NWT said that Jesus was to be worshipped (Heb. 1:6), but the WTS changed the NWT so that later editions would support its doctrines. The translators now decided to render the Greek word for "worship" (proskuneo) as "do obeisance" every time it is applied to Jesus, but as "worship" when modifying Jehovah. If the translators were consistent, then Jesus would be given the worship due to God in Matthew. 14:33, 28:9, 28:17, Luke 24:52, John 9:38, and Hebrews 1:6.
This is not to say that the RC has no useful or valid arguments against the Watchtower. I'm just pointing out that RC dogma and apologetic practice prevents them from using this argument.