Short answer
God (﷾) alone. Satan once asked Jesus to bow down to him. Jesus answered from the Law of Moses, the first five books of the Bible. He said: "Thou shalt worship the Lord thy God, and him only shalt thou serve". He told a Samaritan woman that true worshippers "shall worship the Father". He also counted himself among the worshippers: "we know what we worship". As John's Gospel tells it, after the resurrection he called God "my God, and your God". One who worships God (﷾) and calls Him "my God" is not the God (﷾) he worships. Islam teaches the same. The Qur'an records Jesus telling his people, "worship Allah, my Lord and your Lord".
Full explanation
Jesus' answer to Satan
Satan offered Jesus the kingdoms of the world if he would fall down and worship him. Matthew and Luke both give the same answer: worship belongs to God (﷾), and to God (﷾) only. Jesus did not say "worship me". He sent worship past himself to God (﷾).
“And saith unto him, All these things will I give thee, if thou wilt fall down and worship me.”
“Then saith Jesus unto him, Get thee hence, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve.”
“And Jesus answered and said unto him, Get thee behind me, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve.”
The Law Jesus was quoting
Jesus' answer comes from the Law of Moses, and behind it stands a chain of commands. The first of the Ten Commandments forbids any other god. God (﷾) calls Himself "Jealous" when He renews His covenant, His agreement, with Israel. Moses gives Israel the creed of one God (﷾), a statement of belief. Jesus himself called it the first of all the commandments. A few verses later comes the command Jesus quoted to Satan, with its warning against other gods. The prophet Isaiah adds that God (﷾) will not give His glory to another.
“Thou shalt have no other gods before me. Thou shalt not make unto thee any graven image, or any likeness of any thing that is in heaven above, or that is in the earth beneath, or that is in the water under the earth: Thou shalt not bow down thyself to them, nor serve them: for I the Lord thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me;”
“For thou shalt worship no other god: for the Lord, whose name is Jealous, is a jealous God:”
“Hear, O Israel: The Lord our God is one Lord:”
“And Jesus answered him, The first of all the commandments is, Hear, O Israel; The Lord our God is one Lord:”
“Thou shalt fear the Lord thy God, and serve him, and shalt swear by his name. Ye shall not go after other gods, of the gods of the people which are round about you; (For the Lord thy God is a jealous God among you) lest the anger of the Lord thy God be kindled against thee, and destroy thee from off the face of the earth.”
“I am the Lord: that is my name: and my glory will I not give to another, neither my praise to graven images.”
Jesus stands among the worshippers
A Samaritan woman, from a neighbouring people, asked Jesus about worship. He said "we know what we worship". In this way he counted himself and his own people as worshippers of God (﷾). He also said the true worshippers worship the Father. In John's Gospel, on the morning Christians call the resurrection, he calls God "my God, and your God". In Revelation, the last book of the Bible, he speaks from heaven and says "my God" four times in one verse.
“Ye worship ye know not what: we know what we worship: for salvation is of the Jews.”
“But the hour cometh, and now is, when the true worshippers shall worship the Father in spirit and in truth: for the Father seeketh such to worship him.”
“Jesus saith unto her, Touch me not; for I am not yet ascended to my Father: but go to my brethren, and say unto them, I ascend unto my Father, and your Father; and to my God, and your God.”
“Him that overcometh will I make a pillar in the temple of my God, and he shall go no more out: and I will write upon him the name of my God, and the name of the city of my God, which is new Jerusalem, which cometh down out of heaven from my God: and I will write upon him my new name.”
The verses Christians cite
Christians reply that the New Testament shows Jesus receiving worship. The letter to the Hebrews tells the angels of God (﷾) to worship him. They say the disciples worshipped him after the resurrection. Christians read this as worship given to God the Son.
“And again, when he bringeth in the firstbegotten into the world, he saith, And let all the angels of God worship him.”
“And when they saw him, they worshipped him: but some doubted.”
What "worship" means in those verses
The Greek verb in these verses is proskuneo. It is used for the worship of God (﷾). But the Bible also uses it for bowing down before a king or an honoured man. So the word alone does not decide which is meant. It is the very word in Jesus' answer to Satan, "Thou shalt worship the Lord thy God". It is also used for a servant falling down before a king in one of Jesus' parables. And it is used for enemies who will bow before the feet of the Christians of Philadelphia, a city in what is now Turkey. No one takes that king or those Christians to be God. Now look at Hebrews itself. Three verses after the angels are told to bow, the letter says to Jesus: "God, even thy God, hath anointed thee". Just before that, Hebrews 1:8 does call him "O God". But verses 8 and 9 quote Psalm 45, a wedding song for a king of Israel. The king addressed as "O God" in that psalm still has "thy God" who anointed him. The same psalm tells the king's bride, "he is thy Lord; and worship thou him". A man can be bowed to without being God.
“The servant therefore fell down, and worshipped him, saying, Lord, have patience with me, and I will pay thee all.”
“Behold, I will make them of the synagogue of Satan, which say they are Jews, and are not, but do lie; behold, I will make them to come and worship before thy feet, and to know that I have loved thee.”
“Then saith Jesus unto him, Get thee hence, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve.”
“But unto the Son he saith, Thy throne, O God, is for ever and ever: a sceptre of righteousness is the sceptre of thy kingdom. Thou hast loved righteousness, and hated iniquity; therefore God, even thy God, hath anointed thee with the oil of gladness above thy fellows.”
“Thy throne, O God, is for ever and ever: the sceptre of thy kingdom is a right sceptre. Thou lovest righteousness, and hatest wickedness: therefore God, thy God, hath anointed thee with the oil of gladness above thy fellows.”
“So shall the king greatly desire thy beauty: for he is thy Lord; and worship thou him.”
The glory Jesus had before the world was
Christians answer Isaiah 42:8 with John 17:5. There Jesus speaks of the glory he had with the Father before the world was. But in that same verse Jesus asks the Father to give it: "glorify thou me". Later in the same prayer he calls it "my glory, which thou hast given me". And he passes it on to his disciples: "the glory which thou gavest me I have given them". A glory that was given to Jesus, and that he gave on to others, is not the glory God (﷾) will not give to another.
“And now, O Father, glorify thou me with thine own self with the glory which I had with thee before the world was.”
“Father, I will that they also, whom thou hast given me, be with me where I am; that they may behold my glory, which thou hast given me: for thou lovedst me before the foundation of the world.”
“And the glory which thou gavest me I have given them; that they may be one, even as we are one:”
“I am the Lord: that is my name: and my glory will I not give to another, neither my praise to graven images.”
Worship built on the commandments of men
Jesus condemned worship that teaches "for doctrines the commandments of men". He never used the word Trinity. He never told anyone to worship three persons in one God (﷾). The creed he gave was "The Lord our God is one Lord". The Church's doctrine of the Trinity was set out by councils of bishops, at Nicaea in 325 and Constantinople in 381.
“But in vain they do worship me, teaching for doctrines the commandments of men.”
“And Jesus answered him, The first of all the commandments is, Hear, O Israel; The Lord our God is one Lord:”
The creed opens: "We believe in one God, the Father Almighty, maker of all things visible and invisible". The council confessed the Son as begotten of the Father, true God of true God, and "of one substance" (homoousios) with the Father, and condemned those who said there was a time when he was not.
The council confessed the Holy Spirit as the Lord and Giver of life, who proceeds from the Father, and who with the Father and the Son together is worshipped and glorified.
What the Qur'an says Jesus taught
The Qur'an records Jesus telling the Children of Israel to worship Allah (﷾), "my Lord and your Lord". It says Christ never disdained to be a servant of Allah (﷾) and to worship Him.
“They do blaspheme who say: "Allah is Christ the son of Mary." But said Christ: "O Children of Israel! worship Allah, my Lord and your Lord." Whoever joins other gods with Allah,- Allah will forbid him the garden, and the Fire will be his abode. There will for the wrong-doers be no one to help.”
“Verily Allah is my Lord and your Lord: Him therefore serve ye: this is a Way that is straight.”
“Christ disdaineth nor to serve and worship Allah, nor do the angels, those nearest (to Allah): those who disdain His worship and are arrogant,-He will gather them all together unto Himself to (answer).”
Verse by verse
Hebrews 1:6 — Epistle to the Hebrews, chapter 1, verse 6
“And again, when he bringeth in the firstbegotten into the world, he saith, And let all the angels of God worship him.”
Cited for
The angels are told to worship the Son, and only God may be worshipped, so the Son is God.
The response
The Greek verb, proskuneo, is used for worshipping God (﷾). But it is also used for bowing before kings and even before believers, so the word alone proves nothing. Three verses later the same letter says to the Son, "God, even thy God, hath anointed thee". Verse 8 does call him "O God", but verses 8 and 9 quote Psalm 45, a wedding song for a king of Israel. The king addressed as "O God" in that psalm still has "thy God" who anointed him. The same psalm tells the king's bride, "he is thy Lord; and worship thou him". A man can be bowed to without being God. The one who is anointed has a God above him.
Where it lands — The chapter honours one whom God (﷾) anointed. It does not make him the God who anointed him.
John 17:5 — Gospel of John, chapter 17, verse 5
“And now, O Father, glorify thou me with thine own self with the glory which I had with thee before the world was.”
Cited for
God gives His glory to no other, yet Jesus had glory with the Father before the world was. So Jesus shares God's own glory and is God.
The response
In the same verse Jesus asks the Father to glorify him, so the glory is something he receives. Later in the prayer he calls it "my glory, which thou hast given me". He also says he has given the same glory to his disciples. Nobody takes the disciples to share God's (﷾) being. A glory that can be given to Jesus and handed on to others is not the glory God (﷾) keeps for Himself.
Where it lands — John 17 describes a glory given to Jesus and shared with his followers. It does not meet Isaiah 42:8, where God (﷾) keeps His glory for Himself.
John 5:23 — Gospel of John, chapter 5, verse 23
“That all men should honour the Son, even as they honour the Father. He that honoureth not the Son honoureth not the Father which hath sent him.”
Cited for
Jesus says all should honour the Son as they honour the Father, which is worship.
The response
The verse says "honour", not worship, and it gives the reason in the same breath: the Son is honoured as the one the Father sent. The next words are "He that honoureth not the Son honoureth not the Father which hath sent him". A messenger is honoured for the sake of the one who sent him. John's Gospel has Jesus say that the true worshippers shall worship the Father.
Where it lands — Honouring the one God (﷾) sent is not worshipping him as God.
Matthew 28:17 — Gospel of Matthew, chapter 28, verse 17
“And when they saw him, they worshipped him: but some doubted.”
Cited for
The disciples worshipped Jesus after the resurrection, and he accepted it.
The response
The word Matthew uses is the one used for bowing before a king or a man of honour. So it does not show that they took him for God. Accepting it proves nothing either. Nebuchadnezzar, king of Babylon about 600 years before Jesus, fell on his face and worshipped Daniel. The Bible records no refusal, and no one takes Daniel for God. In John's Gospel, Jesus sent word to the disciples that he was going to "my God, and your God".
Where it lands — Bowing to Jesus does not turn him into the God (﷾) he himself called "my God".
Perspectives
Mainstream Christian
God alone is to be worshipped, and Jesus is worshipped because he is God the Son, one in being with the Father. The New Testament shows angels and disciples worshipping him.
Hebrews 1:6 tells the angels of God to worship the Son, which Christians read as worship due to God.
Rebuttal
The Greek word, proskuneo, is also used for bowing before kings and believers, so it proves nothing alone. Three verses later the letter says to the Son, "God, even thy God, hath anointed thee". Verse 8 does call him "O God", but it quotes Psalm 45, said to a king of Israel who still has a God above him.
After the resurrection the disciples worshipped Jesus, which Christians read as recognising him as God.
Rebuttal
Matthew uses the word for bowing before a king or an honoured man. Nebuchadnezzar, king of Babylon about 600 years before Jesus, fell on his face and worshipped Daniel, and no one takes Daniel for God. In John's Gospel, Jesus sends word that he is going to "my God, and your God".
The Islamic perspective
Worship belongs to God (﷾) alone. Jesus taught this, practised it and quoted the Law of Moses for it. He was a servant who worshipped God (﷾), not the God (﷾) who is worshipped.
When Satan asked for worship, Jesus answered that God (﷾) alone is to be worshipped and served.
Jesus was quoting the Law of Moses. It forbids any other object of worship, and calls God jealous of His worship.
Suppose Jesus received the worship that belongs to God (﷾) alone. Then his followers would be breaking the Law he quoted to Satan.
Jesus called the creed of one God (﷾) the first of all the commandments.
God (﷾) says He will not give His glory to another.
In John 17 Jesus asks the Father for glory. He calls it glory the Father gave him, and says he has given it to his disciples.
This glory was given to Jesus and passed on to others. So it is not the glory God (﷾) keeps for Himself in Isaiah 42:8.
Jesus said the true worshippers worship the Father, and counted himself among those who worship.
Jesus calls the Father "my God" in John's Gospel, on the morning Christians call the resurrection, and again in Revelation.
One who has a God is not that God.
The Greek word translated "worship" for Jesus is also used for bowing before a king and before ordinary believers.
Jesus condemned worship that teaches for doctrines the commandments of men.
Jesus never taught worship of a Trinity; his creed was "The Lord our God is one Lord". Worship built on the councils' wording of 325 and 381 rests on the teaching of men.
The Qur'an teaches that Jesus told his people to worship Allah (﷾), his Lord and theirs. He was himself a worshipper of Allah (﷾).